分野別セミナー

＊幾何学セミナーはグローバルCOEプログラム「マス・フォア・インダストリ」
の活動の一環として行われております。

概要：
In this talk, I shall discuss the mean curvature flow of spacelike
graphs in curved pseudo-Riemannian manifolds. When the ambient space is
a pseudo-Riemannian product of two Riemannian manifolds whose curvature
tensors satisfy some conditions, I shall prove that the mean curvature
flow remains a spacelike graph and exists for all time, if the initial
spacelike graph is compact. If the first Riemannian manifold in the
product has positive Ricci curvature everywhere, the mean curvature flow
converges to a unique slice. Since the submanifold of mean curvature
zero is the stable solution of mean curvature flow, I shall give several
Bernstein type results for spacelike graph submanifolds immersed in
curved pseudo-Riemannian manifolds.