In this note, we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature. Like the Michale-Simon Sobolev inequality, this inequality contains a term involving the mean curvature.
Yuxin Dong
,
Hezi Lin
,
Lingen Lu
. THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE*[J]. Acta mathematica scientia, Series B, 2024
, 44(1)
: 189
-194
.
DOI: 10.1007/s10473-024-0110-6
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