Mathematische Annalen

, Volume 361, Issue 3–4, pp 725–740 | Cite as

Evolution of contractions by mean curvature flow

  • Andreas Savas-HalilajEmail author
  • Knut Smoczyk


In this article we investigate length decreasing maps \(f:M\rightarrow N\) between Riemannian manifolds \(M\), \(N\) of dimensions \(m\ge 2\) and \(n\), respectively. Assuming that \(M\) is compact and \(N\) is complete such that
$$\begin{aligned} \sec _M>-\sigma \quad \text {and}\quad {\mathrm{Ric }}_M\ge (m-1)\sigma \ge (m-1)\sec _N\ge -\mu , \end{aligned}$$
where \(\sigma \), \(\mu \) are positive constants, we show that the mean curvature flow provides a smooth homotopy of \(f\) into a constant map.

Mathematics Subject Classification

53C44 53C42 57R52 35K55 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institut für Differentialgeometrie and Riemann Center for Geometry and PhysicsLeibniz Universität HannoverHannoverGermany

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