Positive solutions to Schrödinger equations and geometric applications
2020 ◽
Vol 0
(0)
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Keyword(s):
AbstractA variant 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.
2014 ◽
Vol 51
(1)
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pp. 213-219
2012 ◽
Vol 09
(05)
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pp. 1250049
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2013 ◽
Vol 25
(1)
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pp. 668-708
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2014 ◽
Vol 279
(1-2)
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pp. 211-226
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Keyword(s):
2019 ◽
Vol 51
(4)
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pp. 937-955
Keyword(s):
2009 ◽
Vol 110
(2)
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pp. 895-905
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2011 ◽
Vol 61
(6)
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pp. 1033-1044
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Keyword(s):
Keyword(s):
2017 ◽
Vol 146
(1)
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pp. 359-368