Journal of Applied Mathematics

A Note on the Asymptotic Behavior of Parabolic Monge-Ampère Equations on Riemannian Manifolds

Qiang Ru

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 304864, 4 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807897

Digital Object Identifier
doi:10.1155/2013/304864

Mathematical Reviews number (MathSciNet)
MR3035177

Zentralblatt MATH identifier
1266.35112

Citation

Ru, Qiang. A Note on the Asymptotic Behavior of Parabolic Monge-Ampère Equations on Riemannian Manifolds. J. Appl. Math. 2013 (2013), Article ID 304864, 4 pages. doi:10.1155/2013/304864. https://projecteuclid.org/euclid.jam/1394807897


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References

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