TY - GEN A1 - Lokutsievskiy, Lev A1 - Wachsmuth, Gerd A1 - Zelikin, Mikhail T1 - Non-optimality of conical parts for Newton's problem of minimal resistance in the class of convex bodies and the limiting case of infinite height T2 - arXiv N2 - We consider Newton's problem of minimal resistance, in particular we address the problem arising in the limit if the height goes to infinity. We establish existence of solutions and lack radial symmetry of solutions. Moreover, we show that certain conical parts contained in the boundary of a convex body inhibit the optimality in the classical Newton's problem with finite height. This result is applied to certain bodies considered in the literature, which are conjectured to be optimal for the classical Newton's problem, and we show that they are not. KW - Newton’s problem of minimal resistance KW - Conical parts KW - Convex bodies Y1 - 2021 UR - https://arxiv.org/pdf/2009.12128 SP - 1 EP - 20 ER - TY - GEN A1 - Lokutsievskiy, Lev A1 - Wachsmuth, Gerd A1 - Zelikin, Mikhail T1 - Non-optimality of conical parts for Newton's problem of minimal resistance in the class of convex bodies T2 - Calculus of Variations and Partial Differential Equations Y1 - 2022 U6 - https://doi.org/10.1007/s00526-021-02118-y SN - 1432-0835 SN - 0944-2669 VL - 61 IS - 1 ER -