2011/08/30 by Alexander Plakhov
Mathematics · #Point processes and geometric inequalities #Geometric Analysis and Curvature Flows #History and Theory of Mathematics
paper · pdf · doi:10.4153/cjm-2011-070-9
Abstract A body moves in a rare fied medium composed of point particles at rest. The particles make elastic reflections when colliding with the body surface and do not interact with each other. We consider a generalization of Newton’s minimal resistance problem: given two bounded convex bodies C 1 and C 2 ℝ 3 such that C 1 ⊂ c 2 ⊂ and , minimize the resistance in the class of connected bodies B such that C 1 ⊂ B ⊂ C 1 . We prove that the infimum of resistance is zero; that is, there exist ”almost perfectly streamlined” bodies.