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June 2015 Minimal unfolded regions of a convex hull and parallel bodies
Jun O'HARA
Hokkaido Math. J. 44(2): 175-183 (June 2015). DOI: 10.14492/hokmj/1470053289

Abstract

The minimal unfolded region (or the heart) of a bounded subset Ω in the Euclidean space is a subset of the convex hull of Ω the definition of which is based on reflections in hyperplanes. It was introduced to restrict the location of the points that give extreme values of certain functions, such as potentials whose kernels are monotone functions of the distance, and solutions of differential equations to which Aleksandrov's reflection principle can be applied. We show that the minimal unfolded regions of the convex hull and parallel bodies of Ω are both included in that of Ω.

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Jun O'HARA. "Minimal unfolded regions of a convex hull and parallel bodies." Hokkaido Math. J. 44 (2) 175 - 183, June 2015. https://doi.org/10.14492/hokmj/1470053289

Information

Published: June 2015
First available in Project Euclid: 1 August 2016

zbMATH: 1334.52006
MathSciNet: MR3532105
Digital Object Identifier: 10.14492/hokmj/1470053289

Subjects:
Primary: 31C12, 51F99, 51M16, 52A40

Rights: Copyright © 2015 Hokkaido University, Department of Mathematics

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Vol.44 • No. 2 • June 2015
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