6 papers
An isoperimetric inequality for Neumann eigenvalues with radial log-concave measures
Kui Wang, Xiaomei Sun, Anqiang Zhu
We prove a sharp isoperimetric inequality for the harmonic mean of the first nonzero Neumann eigenvalues of the Witten-Laplacian on origin-symmetric Lipschitz domains in space…
Faber Krahn inequality of Robin eigenvalue of the Weighted Laplacian
Daguang Chen, Kui Wang, Anqiang Zhu
In this paper, we study the isoperimetric inequalities for the Robin eigenvalues of the weighted Laplacian with positive Robin parameter in the Euclidean space and the hyper…
To -logconcavity and beyond: Geometric properties of Dirichlet eigenfunctions
Lei Qin, Jin Sun, Kui Wang
We prove that, on a bounded open convex domain , the first Dirichlet eigenfunction of the Laplacian or the Ornstein--Uhlenbeck operator is -logconcave fo…
An isoperimetric inequality for the second Robin eigenvalue of the Weighted Laplacian
Yi Gao, Kui Wang, Anqiang Zhu
In this paper, we investigate a shape optimization problem for the second Robin eigenvalue of the weighted Laplacian on bounded Lipschitz domains symmetric about the origin. Our ma…
Parabolic Frequency on Gaussian Spaces and Unique Continuation
Jin Sun, Kui Wang
We establish an almost-monotonicity formula for a parabolic frequency on Gaussian spaces for solutions of the Ornstein-Uhlenbeck heat equation with lower-order terms: $$\partial_t…
Sharp Fundamental Gap Estimate on Convex Domains in Gaussian Spaces
Jin Sun, Kui Wang
We prove a sharp lower bound for the fundamental gap on convex domains in Gaussian spaces, the difference between the first two eigenvalues of the Ornstein-Uhlenbeck operator with…