Quantitative Stability of Sobolev Inequalities on Compact Riemannian Manifolds
International Mathematics Research Notices, ISSN: 1687-0247, Vol: 2025, Issue: 1
2025
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New Mathematics Findings from University of Pisa Discussed (Quantitative Stability of Sobolev Inequalities On Compact Riemannian Manifolds)
2025 JAN 10 (NewsRx) -- By a News Reporter-Staff News Editor at Math Daily News -- Fresh data on Mathematics are presented in a new
Article Description
We study quantitative stability results for different classes of Sobolev inequalities on general compact Riemannian manifolds. We prove that, up to constants depending on the manifold, a function that nearly saturates a critical Sobolev inequality is quantitatively W-close to a non-empty set of extremal functions, provided that the corresponding optimal Sobolev constant satisfies a suitable strict bound. The case of sub-critical Sobolev inequalities is also covered. Finally, we discuss degenerate phenomena in our quantitative controls.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85213120027&origin=inward; http://dx.doi.org/10.1093/imrn/rnae269; https://academic.oup.com/imrn/article/doi/10.1093/imrn/rnae269/7924957; https://dx.doi.org/10.1093/imrn/rnae269; https://academic.oup.com/imrn/article-abstract/2025/1/rnae269/7924957?redirectedFrom=fulltext
Oxford University Press (OUP)
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