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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.

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