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arXiv · 2310.02808

Probabilistic Method to Fundamental gap problems on the sphere

Gunhee Cho·Guofang Wei·Guang Yang
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Abstract

We provide a probabilistic proof of the fundamental gap estimate for Schr\"odinger 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.

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Gunhee Cho, Guofang Wei, Guang Yang. 2023-10-04. Probabilistic Method to Fundamental gap problems on the sphere. https://arxiv.org/abs/2310.02808

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