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THE ISOPERIMETRIC QUOTIENT OF A CONVEX BODY DECREASES MONOTONICALLY UNDER THE EIKONAL ABRASION MODEL

Part of: Equations of mathematical physics and other areas of application General convexity

Published online by Cambridge University Press:  30 August 2018

Gábor Domokos  and
Zsolt Lángi
Gábor Domokos
Affiliation:
MTA-BME Morphodynamics Research Group and Department of Mechanics, Materials and Structures, Budapest University of Technology, Műegyetem rakpart 1-3., Budapest 1111, Hungary email [email protected]
Zsolt Lángi
Affiliation:
MTA-BME Morphodynamics Research Group and Department of Geometry, Budapest University of Technology, Egry József utca 1., Budapest 1111, Hungary email zlangi @math.bme.hu
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Abstract

We show that under the Eikonal abrasion model, prescribing uniform normal speed in the direction of the inward surface normal, the isoperimetric quotient of a convex shape is decreasing monotonically.

MSC classification

Primary: 35Q85: PDEs in connection with astronomy and astrophysics
Secondary: 35Q86: PDEs in connection with geophysics 52A39: Mixed volumes and related topics
Type
Research Article
Information
Mathematika , Volume 65 , Issue 1 , 2019 , pp. 119 - 129
Copyright
Copyright © University College London 2018 

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