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 fo…
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 smoot…
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…
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…
Higher-order dark solitons and oscillatory dynamics in microcavity polariton condensates
Jinming Sun, Manna Chen, Stefan Schumacher +2
Dark solitons carrying quantized phase information arouse great interest in different nonlinear systems. A dark soliton in 1D can be stabilized in microcavity polariton condensates…