caa a22 4500 445836717 CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00209-010-0768-4 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0768-4 Mean curvature flow of spacelike graphs [Elektronische Daten] [Guanghan Li, Isabel Salavessa] We prove the mean curvature flow of a spacelike graph in (Σ1× Σ2, g 1 − g 2) of a map f : Σ1 → Σ2 from a closed Riemannian manifold (Σ1, g 1) with Ricci 1> 0 to a complete Riemannian manifold (Σ2, g 2) with bounded curvature tensor and derivatives, and with sectional curvatures satisfying K 2≤ K 1, remains a spacelike graph, exists for all time, and converges to a slice at infinity. We also show, with no need of the assumption K 2≤ K 1, that if K 1>0, or if Ricci 1>0 and K 2≤ −c, c>0 constant, any map f : Σ1 → Σ2 is trivially homotopic provided f *g 2<ρ g 1 where $${\rho=\min_{\Sigma_1}K_1/\sup_{\Sigma_2}K_2^+\geq 0}$$ , in case K 1>0, and ρ=+∞ in case K 2≤ 0. This largely extends some known results for K i constant and Σ2 compact, obtained using the Riemannian structure of Σ1 × Σ2, and also shows how regularity theory on the mean curvature flow is simpler and more natural in pseudo-Riemannian setting then in the Riemannian one. Springer-Verlag, 2010 Mean curvature flow nationallicence Spacelike submanifold nationallicence Maximum principle nationallicence Homotopic maps nationallicence Li Guanghan School of Mathematics and Computer Science, Hubei University, 430062, Wuhan, People's Republic of China aut Salavessa Isabel Centro de Física das Interacções Fundamentais, Instituto Superior Técnico, Technical University of Lisbon, Edifício Ciência, Piso 3, Av. Rovisco Pais, 1049-001, Lisbon, Portugal aut Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 697-719 0025-5874 269:3-4<697 2011 269 209 https://doi.org/10.1007/s00209-010-0768-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0768-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Li Guanghan School of Mathematics and Computer Science, Hubei University, 430062, Wuhan, People's Republic of China aut NATIONALLICENCE 700 1- Salavessa Isabel Centro de Física das Interacções Fundamentais, Instituto Superior Técnico, Technical University of Lisbon, Edifício Ciência, Piso 3, Av. Rovisco Pais, 1049-001, Lisbon, Portugal aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 697-719 0025-5874 269:3-4<697 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer