@misc{SauvignySchulzStroehmeretal., author = {Sauvigny, Friedrich and Schulz, Friedmar and Str{\"o}hmer, Gerhard and Friedrich, Tomi}, title = {Professor Heinz on the occasion of his 85th birthday}, language = {en} } @incollection{Sauvigny, author = {Sauvigny, Friedrich}, title = {Global C hoch (2+alpha)- estimates for conformal maps}, series = {Geometric analysis and nonlinear partial differential equations}, booktitle = {Geometric analysis and nonlinear partial differential equations}, edition = {1. Auflage}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {978-3-540-44051-2}, pages = {105 -- 115}, language = {en} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Partielle Differentialgleichungen der Geometrie und der Physik 1 - Grundlagen und Integraldarstellungen : unter Ber{\"u}cksichtigung der Vorlesungen von E. Heinz}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {3-540-20453-9}, pages = {XII, 417}, abstract = {Dieses zweib{\"a}ndige Lehrbuch stellt das Gesamtgebiet der partiellen Differentialgleichungen - vom elliptischen, parabolischen und hyperbolischen Typ - in zwei und mehreren Ver{\"a}nderlichen vor. In diesem Band werden die Differentialgleichungen mit Integraldarstellungen behandelt, w{\"a}hrend im n{\"a}chsten Band funktionalanalytische L{\"o}sungsmethoden vorgestellt werden.}, language = {de} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Partielle Differentialgleichungen der Geometrie und der Physik 2 - Funktionalanalytische L{\"o}sungsmethoden : unter Ber{\"u}cksichtigung der Vorlesungen von E. Heinz}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {3-540-23107-2}, pages = {XII, 350}, abstract = {Dieses zweib{\"a}ndige Lehrbuch stellt das Gesamtgebiet der partiellen Differentialgleichungen - vom elliptischen, parabolischen und hyperbolischen Typ - in zwei und mehreren Ver{\"a}nderlichen vor.W{\"a}hrend im ersten Band Integraldarstellungen im Mittelpunkt standen, werden in diesem Band funktionalanalytische L{\"o}sungsmethoden vorgestellt.}, language = {de} } @article{Sauvigny, author = {Sauvigny, Friedrich}, title = {{\"U}ber nichtlineare elliptische Differentialgleichungssysteme}, language = {de} } @article{Sauvigny, author = {Sauvigny, Friedrich}, title = {Deformation of boundary value problems for surfaces with prescribed mean curvature}, language = {en} } @article{Sauvigny, author = {Sauvigny, Friedrich}, title = {Introduction of isothermal parameters into a Riemannian metric by the continuity method}, language = {en} } @article{SauvignyHildebrandt, author = {Sauvigny, Friedrich and Hildebrandt, Stefan}, title = {Minimal surfaces in a wedge III. Existence of graph solutions and some uniqueness results}, language = {en} } @misc{SauvignyHildebrandt, author = {Sauvigny, Friedrich and Hildebrandt, Stefan}, title = {Minimal surfaces in a wedge IV. H{\"o}lder estimates of the Gauss map and a Bernstein theorem}, series = {Calculus of Variations and Partial Differential Equations}, volume = {8}, journal = {Calculus of Variations and Partial Differential Equations}, number = {1}, issn = {0944-2669}, pages = {71 -- 90}, language = {en} } @article{SauvignyHildebrandt, author = {Sauvigny, Friedrich and Hildebrandt, Stefan}, title = {Minimal surfaces in a wedge II. The edge-creeping phenomenon}, language = {en} } @article{SauvignyHildebrandt, author = {Sauvigny, Friedrich and Hildebrandt, Stefan}, title = {Minimal surfaces in a wedge I. Asymptotic expansions}, language = {en} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Partial Differential Equations 1 - Foundations and Integral Representations}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {3-540-34457-8}, pages = {XIV, 437}, abstract = {Integration and differentiation on manifolds, Functional analytic foundations, Brouwer's degree of mapping, Generalized analytic functions, Potential theory and spherical harmonics, Linear partial differential equations}, language = {en} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Partial Differential Equations 2 - Functional Analytic Methods}, publisher = {World Publishing Corporation Beijing Company}, address = {Beijing, China}, isbn = {978-7-5100-3516-6}, language = {en} } @misc{SauvignyHildebrandt, author = {Sauvigny, Friedrich and Hildebrandt, Stefan}, title = {Relative minimizers of energy are relative minimizers of area}, language = {en} } @book{SauvignyDierkesHildebrandt, author = {Sauvigny, Friedrich and Dierkes, Ulrich and Hildebrandt, Stefan}, title = {Minimal Surfaces}, edition = {2. rev. ed}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-642-11715-2}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Un probl{\`e}me aux limites mixte des surfaces minimales avec une multiple projection plane et le dessin optimal des escaliers tournants}, language = {fr} } @misc{SauvignyHildebrandt, author = {Sauvigny, Friedrich and Hildebrandt, Stefan}, title = {An energy estimate for the difference of solutions for the n-dimensional solution with prescribed mean curvature and removable singularities}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Mixed Boundary Value Problems for Minimal Graphs on a Riemann Surface and Winding Staircases}, language = {en} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Partial Differential Equations 1 - Foundations and Integral Representations}, publisher = {World Publishing Corporation Beijing Company}, address = {Beijing, China}, isbn = {978-7-5100-3517-3}, language = {en} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Partial Differential Equations 2 - Functional Analytic Methods}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {3-540-34461-6}, pages = {XIV, 388}, language = {en} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Partial Differential Equations 1 - Foundations and Integral Representations}, edition = {2. ed.}, publisher = {Springer}, address = {London}, isbn = {978-1-4471-2980-6}, pages = {XV, 447}, language = {en} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Partial Differential Equations 2 - Functional Analytic Methods}, edition = {2. ed.}, publisher = {Springer}, address = {London}, isbn = {978-1-447-12983-7}, pages = {XVI, 453}, language = {en} } @phdthesis{Sauvigny, author = {Sauvigny, Friedrich}, title = {Fl{\"a}chen vorgeschriebener mittlerer Kr{\"u}mmung mit eineindeutiger Projektion auf eine Ebene}, pages = {62}, abstract = {Dissertation an der Mathematisch-Naturwissenschaftlichen Fakult{\"a}t der Georg-August-Universit{\"a}t G{\"o}ttingen.}, language = {de} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Fl{\"a}chen vorgeschriebener mittlerer Kr{\"u}mmung mit eineindeutiger Projektion auf eine Ebene}, series = {Mathematische Zeitschrift}, volume = {180}, journal = {Mathematische Zeitschrift}, number = {1}, issn = {0025-5874}, pages = {41 -- 67}, language = {de} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {On the total number of branch points of quasi-minimal surfaces bounded by a polygon}, series = {Analysis}, volume = {8}, journal = {Analysis}, issn = {0174-4747}, pages = {297 -- 304}, language = {en} } @phdthesis{Sauvigny, author = {Sauvigny, Friedrich}, title = {A-Priori-Absch{\"a}tzungen der Hauptkr{\"u}mmungen f{\"u}r Immersionen vom Mittleren-Kr{\"u}mmungs-Typ mittels Uniformisierung und S{\"a}tze vom Bernstein-Typ}, pages = {78}, abstract = {Habilitationsschrift am Fachbereich Mathematik an der Georg-August-Universit{\"a}t G{\"o}ttingen.}, language = {de} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {On immersions of constant mean curvature: Compactness results and finiteness theorems for Plateau's problem}, series = {Archive for Rational Mechanics and Analysis}, volume = {110}, journal = {Archive for Rational Mechanics and Analysis}, number = {2}, issn = {0003-9527}, pages = {125 -- 140}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Curvature estimates for immersions of minimal surface type via uniformization and theorems of Bernstein type}, series = {Manuscripta Mathematica}, volume = {67}, journal = {Manuscripta Mathematica}, issn = {0025-2611}, pages = {69 -- 97}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {A priori estimates of the principal curvatures for immersions of prescribed mean curvature and theorems of Bernstein type}, series = {Mathematische Zeitschrift}, volume = {205}, journal = {Mathematische Zeitschrift}, number = {1}, issn = {0025-5874}, pages = {567 -- 582}, language = {en} } @misc{SauvignyHildebrandt, author = {Sauvigny, Friedrich and Hildebrandt, Stefan}, title = {Embeddedness and uniqueness of minimal surfaces solving a partially free boundary value problem}, series = {Journal f{\"u}r die reine und angewandte Mathematik}, volume = {422}, journal = {Journal f{\"u}r die reine und angewandte Mathematik}, issn = {0075-4102}, pages = {69 -- 89}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {A new proof of the gradient estimate for graphs of prescribed mean curvature}, series = {Manuscripta mathematica}, volume = {74}, journal = {Manuscripta mathematica}, number = {1}, issn = {0025-2611}, pages = {83 -- 86}, language = {en} } @misc{SauvignyHildebrandt, author = {Sauvigny, Friedrich and Hildebrandt, Stefan}, title = {On one-to-one harmonic mappings and minimal surfaces}, series = {Nachrichten der Akademie der Wissenschaften zu G{\"o}ttingen, 2. Mathematisch-Physikalische Klasse}, journal = {Nachrichten der Akademie der Wissenschaften zu G{\"o}ttingen, 2. Mathematisch-Physikalische Klasse}, number = {3}, issn = {0065-5295}, pages = {73 -- 93}, language = {en} } @misc{SauvignyHildebrandt, author = {Sauvigny, Friedrich and Hildebrandt, Stefan}, title = {Uniqueness of stable minimal surfaces with partially free boundaries}, series = {Journal of the Mathematical Society of Japan}, volume = {47}, journal = {Journal of the Mathematical Society of Japan}, number = {3}, issn = {0025-5645}, pages = {423 -- 440}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Die zweite Variation von Minimalfl{\"a}chen im R-hoch-p mit polygonalem Rand}, series = {Mathematische Zeitschrift}, volume = {189}, journal = {Mathematische Zeitschrift}, issn = {0025-5874}, pages = {167 -- 184}, language = {de} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Ein Eindeutigkeitssatz f{\"u}r Minimalfl{\"a}chen im R-hoch-p mit polygonalem Rand}, series = {Journal f{\"u}r die reine und angewandte Mathematik}, volume = {358}, journal = {Journal f{\"u}r die reine und angewandte Mathematik}, issn = {0075-4102}, pages = {92 -- 96}, language = {de} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {On the Morse index of minimal surfaces in R-hoch-p with polygonal boundaries}, series = {Manuscripta Mathematica}, volume = {53}, journal = {Manuscripta Mathematica}, issn = {0025-2611}, pages = {167 -- 197}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {{\"U}ber das Plateausche Problem f{\"u}r Wendelkurven}, series = {Mathematische Semesterberichte}, volume = {60}, journal = {Mathematische Semesterberichte}, number = {2}, issn = {0720-728X}, pages = {151 -- 183}, language = {de} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Analysis : Grundlagen, Differentiation, Integrationstheorie, Differentialgleichungen, Variationsmethoden}, publisher = {Springer Spektrum}, address = {Berlin [u.a.]}, isbn = {978-3-642-41506-7}, pages = {XV, 512 S.}, language = {de} } @incollection{HildebrandtSauvigny, author = {Hildebrandt, Stefan and Sauvigny, Friedrich}, title = {On Plateaus's problem in Riemannian manifolds}, series = {Proceedings of the St. Petersburg mathematical society : advances in mathematical analysis of partial differential equations ; dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya}, booktitle = {Proceedings of the St. Petersburg mathematical society : advances in mathematical analysis of partial differential equations ; dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya}, editor = {Apushkinskaya, Darya and Nazarov, Alexander I.}, publisher = {American Mathematical Soc.}, address = {Providence, RI}, isbn = {978-1-4704-1551-8}, pages = {141 -- 152}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Surfaces of prescribed mean curvature H(x,y,z) with one-to-one central projection onto a plane}, series = {Pacific Journal of Mathematics}, volume = {281}, journal = {Pacific Journal of Mathematics}, number = {2}, issn = {0030-8730}, doi = {10.2140/pjm.2016.281.481}, pages = {481 -- 509}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Maximum Principle for H-Surfaces in the Unit Cone and Dirichlet's Problem for their Equation in Central Projection}, series = {Milan Journal of Mathematics}, volume = {84}, journal = {Milan Journal of Mathematics}, number = {1}, issn = {1424-9286}, doi = {10.1007/s00032-016-0250-9}, pages = {91 -- 104}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Multiple solutions for the nonparametric Plateau problem within the Euclidean space Rᴾ of arbitrary dimension}, series = {Calculus of Variations and Partial Differential Equations}, volume = {55}, journal = {Calculus of Variations and Partial Differential Equations}, number = {6, Artikel 140}, issn = {0944-2669}, doi = {10.1007/s00526-016-1087-3}, pages = {1 -- 28}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Solution of boundary value problems for surfaces of prescribed mean curvature H (x, y, z) with 1-1 central projection via the continuity method}, series = {Lithuanian mathematical journal}, volume = {58}, journal = {Lithuanian mathematical journal}, number = {3}, issn = {1573-8825}, doi = {10.1007/s10986-018-9399-y}, pages = {320 -- 328}, abstract = {When we consider surfaces of prescribed mean curvature H with a one-to-one orthogonal projection onto a plane, we have to study the nonparametric H-surface equation. Now the H-surfaces with a one-to-one central projection onto a plane lead to an interesting elliptic differential equation, which has been discovered for the case H = 0 already by T. Rad{\´o} in 1932. We establish the uniqueness of the Dirichlet problem for this H-surface equation in central projection and develop an estimate for the maximal deviation of large H-surfaces from their boundary values, resembling an inequality by J. Serrin from 1969. We solve the Dirichlet problem for nonvanishing H with compact support via a nonlinear continuity method. Here we introduce conformal parameters into the surface and study the well-known H-surface system. Then we combine these investigations with a differential equation for its unit normal, which has been developed by the author for variable H in 1982. Furthermore, we construct large H-surfaces bounding extreme contours by an approximation. Here we only provide an overview on the relevant proofs; for the more detailed derivations of our results, we refer the readers to the author's investigations in the Pacific Journal of Mathematics and the Milan Journal of Mathematics.}, language = {en} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Spektraltheorie selbstadjungierter Operatoren im Hilbertraum und elliptischer Differentialoperatoren}, publisher = {Springer Spektrum}, address = {Heidelberg [u.a]}, isbn = {978-3-662-58069-1}, doi = {10.1007/978-3-662-58069-1}, pages = {xi, 259}, language = {de} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Analysis}, edition = {2}, publisher = {Springer Berlin Heidelberg}, address = {Berlin, Heidelberg}, isbn = {978-3-662-69864-8}, doi = {10.1007/978-3-662-69865-5}, pages = {625}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Minimal graphs in Riemannian spaces}, series = {Calculus of Variations and Partial Differential Equations}, volume = {63}, journal = {Calculus of Variations and Partial Differential Equations}, number = {5}, issn = {1432-0835}, doi = {10.1007/s00526-024-02704-w}, pages = {1 -- 47}, language = {en} }