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

[摘要] 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)in𝕄×(0,∞),φ(x,0)=φ0(x)in𝕄, where𝕄is a compact complete Riemannian manifold,λis a positive real parameter, andφ0(x):𝕄→ℝis a smooth function. We show a meaningful asymptotic result which is more general than those in Huisken, 1997.

[学科分类] 应用数学