Archive for Rational Mechanics and Analysis

, Volume 204, Issue 3, pp 917–944 | Cite as

Non-Contraction of Heat Flow on Minkowski Spaces

  • Shin-ichi Ohta
  • Karl-Theodor Sturm


We study contractivity properties of gradient flows for functions on normed spaces or, more generally, on Finsler manifolds. Contractivity of the flows turns out to be equivalent to a new notion of convexity for the functions. This is different from the usual convexity along geodesics in non-Riemannian Finsler manifolds. As an application, we show that the heat flow on Minkowski normed spaces other than inner product spaces is not contractive with respect to the quadratic Wasserstein distance.


Riemannian Manifold Minkowski Space Relative Entropy Variation Formula Finsler Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of MathematicsKyoto UniversityKyotoJapan
  2. 2.Max-Planck-Institut für MathematikBonnGermany
  3. 3.Institut für Angewandte MathematikUniversität BonnBonnGermany

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