Probabilistic Method to Fundamental gap problems on the sphere

2023/10/04 by Gunhee Cho, Cho, Gunhee, Guofang Wei +3 · 3 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2310.02808

Abstract

We provide a probabilistic proof of the fundamental gap estimate for Schrödinger operators in convex domains on the sphere, which extends the probabilistic proof of F. Gong, H. Li, and D. Luo for the Euclidean case. Our results further generalize the results achieved for the Laplacian by S. Seto, L. Wang, and G. Wei, as well as by C. He, G. Wei, and Qi S. Zhang. The essential ingredient in our analysis is the reflection coupling method on Riemannian manifolds.

Cited by

• Constant potentials do not minimise the fundamental gap on convex domains in hyperbolic space
• Deterministic--Distance Couplings of Brownian Motions on Radially Isoparametric Manifolds
• Sharp Fundamental Gap Estimate on Convex Domains in Gaussian Spaces

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• Sharp Fundamental Gap Estimate on Convex Domains of Sphere
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