On Surface Measures on Convex Bodies and Generalizations of Known Tangential Identities

Authors: Johan Aspegren

One theme of this paper is to extend known results from polygons and balls to the general convex bodies in n− dimensions. An another theme stems from approximating a convex surface with polytope surface. Our result gives a sufficient and necessary condition for an natural approximation method to succeed (in principle) in the case of surfaces of convex bodies. Thus, Schwartz`s paradox does not affect our method. This allows us to denefine certain surface measures on surfaces of convex bodies in a novel and simple way.

Comments: 12 Pages.

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Submission history

[v1] 2018-05-01 00:29:25
[v2] 2018-05-03 15:13:00 (removed)
[v3] 2018-05-06 01:48:26
[v4] 2018-05-14 17:34:50 (removed)
[v5] 2018-05-20 22:09:51
[v6] 2018-05-22 11:28:23
[v7] 2018-05-30 16:22:45
[v8] 2019-05-30 19:33:17
[v9] 2019-09-21 11:22:17
[vA] 2019-12-02 13:56:27

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