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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…
math.DG2014
Rigidity theorems of complete Kähler-Einstein manifolds and complex space forms
Tian Chong, Yuxin Dong, Hezi Lin +1
We derive some elliptic differential inequalities from the Weitzenböck formulas for the traceless Ricci tensor of a Kähler manifold with constant scalar curvature and the Bochner t…
math.DG2012
Monotonicity formulae, vanishing theorems and some geometric applications
Yuxin Dong, Hezi Lin
Using the stress energy tensor, we establish some monotonicity formulae for vector bundle-valued p-forms satisfying the conservation law, provided that the base Riemannian (resp. K…