Archiv der Mathematik

, Volume 90, Issue 5, pp 450–460 | Cite as

Is quasi-concavity preserved by heat flow?



We investigate on the preservation of spatial quasi-concavity of the initial datum by the solutions of the heat equation and we give negative results in dimension N ≥ 2.

Mathematics Subject Classification (2000).

35K05 52A01 35B05 35B30 


Quasi-concavity heat equation level sets convexity 


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Copyright information

© Birkhaeuser 2008

Authors and Affiliations

  1. 1.Mathematical Institute Tohoku University AobaSendaiJapan
  2. 2.Dipartimento di Matematica ‘U. Dini’ Viale Morgagni 67/AFirenzeItaly

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