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2003 ◽  
Vol 46 (1) ◽  
pp. 117-146 ◽  
Author(s):  
Christophe Brouttelande

AbstractThe best-constant problem for Nash and Sobolev inequalities on Riemannian manifolds has been intensively studied in the last few decades, especially in the compact case. We treat this problem here for a more general family of Gagliardo–Nirenberg inequalities including the Nash inequality and the limiting case of a particular logarithmic Sobolev inequality. From the latter, we deduce a sharp heat-kernel upper bound.AMS 2000 Mathematics subject classification: Primary 58J05


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