Probabilistic method to fundamental gap problems on the sphere
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- by Gunhee Cho, Guofang Wei and Guang Yang;
- Trans. Amer. Math. Soc. 378 (2025), 317-337
- DOI: https://doi.org/10.1090/tran/9285
- Published electronically: October 17, 2024
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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 [Potential Anal. 44 (2016), pp. 423–442] for the Euclidean case. Our results further generalize the results achieved for the Laplacian by S. Seto, L. Wang, and G. Wei [J. Differential Geom. 112 (2019), pp. 347–389], as well as by C. He, G. Wei, and Qi S. Zhang [Amer. J. Math. 142 (2020), pp. 1161–1191]. The essential ingredient in our analysis is the reflection coupling method on Riemannian manifolds.References
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Bibliographic Information
- Gunhee Cho
- Affiliation: Department of Mathematics, University of California, Santa Barbara, Santa Barbara, California 93106
- MR Author ID: 1384289
- ORCID: 0000-0002-8474-4749
- Email: gunhee.cho@math.ucsb.edu
- Guofang Wei
- Affiliation: Department of Mathematics, University of California, Santa Barbara, Santa Barbara, California 93106
- MR Author ID: 252129
- ORCID: 0000-0003-4165-0774
- Email: wei@math.ucsb.edu
- Guang Yang
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- Email: yang2220@purdue.edu
- Received by editor(s): October 9, 2023
- Received by editor(s) in revised form: May 9, 2024
- Published electronically: October 17, 2024
- Additional Notes: The first author was partially supported by AMS Simons travel grant.
The second author was partially supported by NSF DMS grant 2104704. - © Copyright 2024 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 378 (2025), 317-337
- MSC (2020): Primary 60D05, 60Gxx, 53-XX
- DOI: https://doi.org/10.1090/tran/9285
- MathSciNet review: 4840306