Homotopy of area decreasing maps by mean curvature flow

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Original languageEnglish
Pages (from-to)455-473
Number of pages19
JournalAdvances in mathematics
Volume255
Publication statusPublished - 1 Apr 2014

Abstract

Let f : M → N be a smooth area decreasing map between two Riemannian manifolds (M, gM) and (N, gN). Under weak and natural assumptions on the curvatures of (M, gM) and (N, gN), we prove that the mean curvature flow provides a smooth homotopy of f to a constant map.

Keywords

    Area decreasing, Graphs, Homotopy, Maximum principle, Mean curvature flow

ASJC Scopus subject areas

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Homotopy of area decreasing maps by mean curvature flow. / Savas-Halilaj, Andreas; Smoczyk, Knut.
In: Advances in mathematics, Vol. 255, 01.04.2014, p. 455-473.

Research output: Contribution to journalArticleResearchpeer review

Savas-Halilaj A, Smoczyk K. Homotopy of area decreasing maps by mean curvature flow. Advances in mathematics. 2014 Apr 1;255:455-473. doi: 10.1016/j.aim.2014.01.014
Savas-Halilaj, Andreas ; Smoczyk, Knut. / Homotopy of area decreasing maps by mean curvature flow. In: Advances in mathematics. 2014 ; Vol. 255. pp. 455-473.
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