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Geometric analysis seminar: Log-Concavity and Fundamental Gaps on Surfaces of Positive Curvature

Author: Lona | Image: Lona

Speaker: Malik Tuerkoen, UCSB

Abstract: The fundamental gap is the difference of the first two eigenvalues of the Laplace operator, which is important both in mathematics and physics and has been extensively studied. For the Dirichlet boundary condition the log-concavity estimate of the first eigenfunction plays a crucial role, which was established for convex domains in the Euclidean space and round sphere. Joint with G. Khan, H. Nguyen and G. Wei, we obtain log-concavity estimates of the first eigenfunction for convex domains in surfaces of positive curvature and consequently establish fundamental gap estimates.