3 papers
math.DG2026
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…
math.DG2025
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…
math.DG2024
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…