Łojasiewicz–Simon gradient inequalities for analytic and Morse–Bott functions on Banach spaces
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This article is published in Crelle's Journal.The article was published on 2020-08-01 and is currently open access. It has received 21 citations till now. The article focuses on the topics: Banach space & Differential geometry.read more
Citations
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On the Łojasiewicz–Simon gradient inequality on submanifolds
TL;DR: In this article, the authors provided sufficient conditions for the Łojasiewicz-Simon gradient inequality to hold on a submanifold of a Banach space and discussed the optimality of their assumptions.
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On the Morse–Bott property of analytic functions on Banach spaces with Łojasiewicz exponent one half
TL;DR: In this article, it was shown that if the Łojasiewicz exponent of an analytic function is equal to one half at a critical point, then the function is Morse-Bott and thus its critical set nearby is an analytic submanifold.
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Resolution of singularities and geometric proofs of the Łojasiewicz inequalities
TL;DR: In this article, Bierstone and Milman gave an elementary geometric, coordinate-based proof of the Łojasiewicz inequalities in the special case where the function is C1 with simple normal crossings.
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Global existence and convergence of a flow to Kazdan-Warner equation with non-negative prescribed function
Linlin Sun,Jingyong Zhu +1 more
TL;DR: Yang and Zhu as mentioned in this paper considered an evolution problem associated to the Kazdan-Warner equation on a closed Riemann surface and proved the global existence and convergence under additional assumptions.
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The Riemannian Quantitative Isoperimetric Inequality
TL;DR: In this article, the Riemannian quantiative isoperimetric inequality is shown to be true generically on a closed manifold, and a modified version of the quantitative isopo-measure inequality holds for a real analytic metric.
References
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Functional Analysis, Sobolev Spaces and Partial Differential Equations
TL;DR: In this article, the theory of conjugate convex functions is introduced, and the Hahn-Banach Theorem and the closed graph theorem are discussed, as well as the variations of boundary value problems in one dimension.
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The Yang-Mills equations over Riemann surfaces
Michael Atiyah,Raoul Bott +1 more
TL;DR: In this article, the Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory, and the main result is that this is a perfect 9 functional provided due account is taken of its gauge symmetry.
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Eigenvalues in Riemannian geometry
TL;DR: The Dirichlet Heat Kernel for Regular Domains as mentioned in this paper is a heat kernel for non-compact manifolds that is based on the Laplacian on forms (LFP).
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Riemannian geometry and geometric analysis
TL;DR: A very readable introduction to Riemannian geometry and geometric analysis can be found in this paper, where the author focuses on using analytic methods in the study of some fundamental theorems in Riemmannian geometry, e.g., the Hodge theorem, the Rauch comparison theorem, Lyusternik and Fet theorem and the existence of harmonic mappings.