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Liouville type theorems on manifolds with nonnegative curvature and strictly convex boundary

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 نشر من قبل Xiaodong Wang
 تاريخ النشر 2019
  مجال البحث
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We prove some Liouville type theorems on smooth compact Riemannian manifolds with nonnegative sectional curvature and strictly convex boundary. This gives a nonlinear generalization in low dimension of the recent sharp lower bound of the first Steklov eigenvalue by Xia-Xiong and verifies partially a conjecture by the third author. As a consequence, we derive several sharp Sobolev trace inequalities on these manifolds.



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