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math.AP2026
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…
math.AP2026
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…
math.AP2025
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…