6 papers
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 for…
Parabolic Frequency for Doubly Nonlinear Equations on Manifolds
Jin Sun, Philipp Sürig
We establish monotonicity formulas for a parabolic frequency function associated with sign-changing solutions to a class of doubly nonlinear parabolic equations of the form $\parti…
Sharp long distance upper bounds for solutions of Leibenson's equation on Riemannian manifolds
Alexander Grigor'yan, Jin Sun, Philipp Sürig
We consider on Riemannian manifolds the Leibenson equation that is also known as a doubly nonlinear evolution equation. We prove sharp upper estimates o…
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…
The hot spots conjecture on Gaussian spaces
Bobo Hua, Jin Sun
We study the hot spots conjecture for domains in the Gaussian space for . Given a bounded domain with a piecewise smooth…