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Title: Local properties of the surface measure of convex bodies
Author: Plakhov, Alexander
Keywords: Convex sets
Blaschke addition
Newton's problems of minimal resistance
Issue Date: 2019
Publisher: Heldermann Verlag
Abstract: It is well known that any measure in S^2 satisfying certain simple conditions is the surface measure of a bounded convex body in R^3. It is also known that a local perturbation of the surface measure may lead to a nonlocal perturbation of the corresponding convex body. We prove that, under mild conditions on the convex body, there are families of perturbations of its surface measure forming line segments, with the original measure at the midpoint, corresponding to {\it local} perturbations of the body. Moreover, there is, in a sense, a huge amount of such families. We apply this result to Newton's problem of minimal resistance for convex bodies.
Peer review: yes
ISSN: 0944-6532
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

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