7 papers
Boundary Perturbations of Steklov Eigenvalues
Lihan Wang
We consider the dependence of non-zero Steklov eigenvalues on smooth perturbations of the domain boundary. We prove that these eigenvalues are generically simple under such boundar…
Upper bound of the counting function of Steklov eigenvalues
Fei He, Lihan Wang
We study the counting function of Steklov eigenvalues on compact manifolds with boundary and obtain its upper bound involving the leading term of Weyl's law. Our estimate can be vi…
Rigidity of complete manifolds with weighted Poincaré inequality
Lihan Wang
We consider complete Riemannian manifolds which satisfy a weighted Poincarè inequality and have the Ricci curvature bounded below in terms of the weight function. When the weight f…
Generic properties of Steklov eigenfunctions
Lihan Wang
Let be a smooth compact manifolds with smooth boundary. We show that for a generic metic on with , the nonzero Steklov eigenvalues are simple. Moreov…
Gradient estimate for harmonic functions on Kähler manifolds
Ovidiu Munteanu, Lihan Wang
We prove a sharp integral gradient estimate for harmonic functions on noncompact Kähler manifolds. As application, we obtain a sharp estimate for the bottom of spectrum of the p-La…
Symplectic Boundary Conditions and Cohomology
Li-Sheng Tseng, Lihan Wang
We introduce new boundary conditions for differential forms on symplectic manifolds with boundary. These boundary conditions, dependent on the symplectic structure, allows us to wr…
Hodge Theory and Symplectic Boundary Conditions
Li-Sheng Tseng, Lihan Wang
We study symplectic Laplacians on compact symplectic manifolds with boundary. These Laplacians are associated with symplectic cohomologies of differential forms and can be of fourt…