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2013 A Note on the Asymptotic Behavior of Parabolic Monge-Ampère Equations on Riemannian Manifolds
Qiang Ru
J. Appl. Math. 2013: 1-4 (2013). DOI: 10.1155/2013/304864

Abstract

We study the asymptotic behavior of the parabolic Monge-Ampère equation φ(x,t)/t=log(det(g(x)+Hessφ(x,t))/detg(x))λφ(x,t) in 𝕄×(0,), φ(x,0)=φ0(x) in 𝕄, where 𝕄 is a compact complete Riemannian manifold, λ is a positive real parameter, and φ0(x):𝕄 is a smooth function. We show a meaningful asymptotic result which is more general than those in Huisken, 1997.

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Qiang Ru. "A Note on the Asymptotic Behavior of Parabolic Monge-Ampère Equations on Riemannian Manifolds." J. Appl. Math. 2013 1 - 4, 2013. https://doi.org/10.1155/2013/304864

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1266.35112
MathSciNet: MR3035177
Digital Object Identifier: 10.1155/2013/304864

Rights: Copyright © 2013 Hindawi

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