https://neckpinch.com/authors/renan-assimos/New arXiv papers by Renan Assimos, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2201.05523/arxiv:2201.05523Fri, 14 Jan 2022 00:00:00 GMTRenan Assimos, Andreas Savas-Halilaj, Knut Smoczyk — We consider the graphical mean curvature flow of strictly area decreasing maps f:M→ N, where M is a compact Riemannian manifold of dimension m>1 and N a complete Riemannian surface of bounded geometry. We prove long-time existence of the flow and that the strictly area decreasing property is preserved, when the bi-Ricci curvature BRic_M of M is bounded from below by the sectional curvature σ_N of N. In addition, we obtain smooth convergence to a minimal map if Ric_M≥sup\0,sup_Nσ_N\. These results significantly improve known results on the graphical mean curvature flow in codimension 2.Mean curvature flowLong-time existence & convergence