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Logarithmic Sobolev inequality in manifolds with nonnegative curvature via the ABP method
Lingen Lu
In this paper, we employ the ABP method developed by Brendle to establish the optimal logarithmic Sobolev inequality on manifolds with nonnegative Ricci curvature, as well as…
Sobolev Inequality In Manifolds With Lower Quadratic Curvature Decay
Tian Chong, Han Luo, Lingen Lu
By using the ABP method developed by Cabré and Brendle, we establish some Sobolev inequalities for compact domains and submanifolds in a complete Riemannian manifold with lower qua…
Hardy type inequalities on manifolds with nonnegative Ricci curvature
Yuxin Dong, Hezi Lin, Lingen Lu
We prove the Heisenberg-Pauli-Weyl inequality, Hardy-Sobolev inequality, and Caffarelli-Kohn-Nirenberg (CKN) inequality on manifolds with nonnegative Ricci curvature and Euclidean…
Sobolev Inequality on Manifolds With Asymptotically Nonnegative Bakry-Émery Ricci Curvature
Yuxin Dong, Hezi Lin, Lingen Lu
In this paper, inspired by [4, 9], we prove a Sobolev inequality on manifolds with density and asymptotically nonnegative Bakry-Émery Ricci curvature.
Sobolev Inequalities In Manifolds With Asymptotically Nonnegative Curvature
Yuxin Dong, Hezi Lin, Lingen Lu
Using the ABP-method as in a recent work by Brendle, we establish some sharp Sobolev and isoperimetric inequalities for compact domains and submanifolds in a complete Riemannian ma…