Non-collapsing for a fully nonlinear inverse curvature flow

Yannan Liu; Hongjie Ju

doi:10.3934/cpaa.2017045

Article Contents

2017, Volume 16, Issue 3: 945-952. Doi: 10.3934/cpaa.2017045

This issue Previous Article Tug-of-war games with varying probabilities and the normalized p(x)-laplacian Next Article Multiple positive standing wave solutions for schrödinger equations with oscillating state-dependent potentials

Non-collapsing for a fully nonlinear inverse curvature flow

Yannan Liu^1, , and
Hongjie Ju^2,

1.
Department of Mathematics, Beijing Technology and Business University, Beijing 100048, China
2.
School of Science, Beijing University of Posts and Telecommunication, Beijing, 100876, China

^* Corresponding author
^* Corresponding author

Received: August 2016

Revised: January 2017

Published: January 2018

The first author is supported by NSFC grant (11201011), NSF of Beijing grant (1132002,1172005). The second author is supported by NSFC grant (11301034,11401527,11471050).

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Abstract

In this paper, we study a fully nonlinear inverse curvature flow in Euclidean space, and prove a non-collapsing property for this flow using maximum principle. Precisely, we show that upon some conditions on speed function, the curvature of the largest touching interior ball is bounded by a multiple of the speed.

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Mathematics Subject Classification: 35K45, 53A05.

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References

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