A note on the asymptotic behavior of parabolic Monge-Ampère equations on Riemannian manifolds (Q2375486)

Summary: We study the asymptotic behavior of the parabolic Monge-Ampère equation \(\partial \varphi(x, t)/\partial t = \log(\det(g(x) + \text{Hess}\varphi(x, t))/\det g(x)) - \lambda \varphi(x, t)\) in \(\mathbb M \times (0, \infty)\), \(\varphi(x, 0) = \varphi_0(x)\) in \(\mathbb M\), where \(\mathbb M\) is a compact complete Riemannian manifold, \(\lambda\) is a positive real parameter, and \(\varphi_0(x) : \mathbb M \to \mathbb R\) is a smooth function. We show a meaningful asymptotic result which is more general than those in \textit{B. Huisken} [J. Funct. Anal. 147, No. 1, 140--163 (1997; Zbl 0895.58053)].