Archiv der Mathematik

, Volume 90, Issue 5, pp 450-460

First online:

Is quasi-concavity preserved by heat flow?

  • Kazuhiro IshigeAffiliated withMathematical Institute Tohoku University Aoba Email author 
  • , Paolo SalaniAffiliated withDipartimento di Matematica ‘U. Dini’ Viale Morgagni 67/A

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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