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Positive solutions to Schrödinger equations and geometric applications
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Munteanu, Ovidiu, Schulze, Felix and Wang, Jiaping (2021) Positive solutions to Schrödinger equations and geometric applications. Journal fur die reine und angewandte Mathematik, 2021 (774). pp. 185-217. doi:10.1515/crelle-2020-0046 ISSN 0075-4102.
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WRAP-positive-solutions-Schrödinger-equations-geometric-applications-Schulze-2020.pdf - Accepted Version - Requires a PDF viewer. Download (392Kb) | Preview |
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Official URL: https://doi.org/10.1515/crelle-2020-0046
Abstract
Avariant of Li-Tam theory, which associates to each end of a complete Riemannian manifold a positive solution of a given Schrödinger equation on the manifold, is developed. It is demonstrated that such positive solutions must be of polynomial growth of fixed order under a suitable scaling invariant Sobolev inequality. Consequently, a finiteness result for the number of ends follows. In the case when the Sobolev inequality is of particular type, the finiteness result is proven directly. As an application, an estimate on the number of ends for shrinking gradient Ricci solitons and submanifolds of Euclidean space is obtained.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Riemannian manifolds, Schrödinger equation, Solitons, Geometry, Differential | ||||||||||||
| Journal or Publication Title: | Journal fur die reine und angewandte Mathematik | ||||||||||||
| Publisher: | Walter de Gruyter & Co | ||||||||||||
| ISSN: | 0075-4102 | ||||||||||||
| Official Date: | May 2021 | ||||||||||||
| Dates: |
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| Volume: | 2021 | ||||||||||||
| Number: | 774 | ||||||||||||
| Page Range: | pp. 185-217 | ||||||||||||
| DOI: | 10.1515/crelle-2020-0046 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
| Date of first compliant deposit: | 11 November 2020 | ||||||||||||
| Date of first compliant Open Access: | 15 December 2021 | ||||||||||||
| RIOXX Funder/Project Grant: |
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