Quantitative Stability of Sobolev Inequalities on Compact Riemannian Manifolds
Year: 2024
Type: article
Abstract: 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 $W^{1,2}$-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.
DOI: 10.1093/imrn/rnae269
Authors: Francesco Nobili, Davide Parise
Institutions: University of Pisa, University of California San Diego
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,534
OpenAlex ID: W4405417424