arXiv subjects

Andrew A Cooper

Publications and source records attributed to Andrew A Cooper.

2 recordsLinked to original sources

arXiv2011

A Compactness Theorem for the Second Fundamental Form

In this note we establish several versions of a compactness theorem for submanifolds. In particular we require only bounds on the second fundamental form and do not assume volume or diameter bounds. As an application we prove a compactness theorem for mean curvature flows and use it to construct smooth blow-up limits as singularity models.

math.DG↗

arXiv2010

A Characterization of the Singular Time of the Mean Curvature Flow

In this note we investigate the behaviour at finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M^m_t\hookrightarrow (N^{m+n}, h). We show that they are characterized by the blow-up of a trace A = H \cdot II of the square of the second fundamental form.

math.DG↗