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arXiv · 2408.06989

Moser-Trudinger inequalities: from local to global

Luigi Fontana·Carlo Morpurgo·Liuyu Qin
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Abstract

Given a general complete Riemannian manifold $M$, we introduce the concept of "local Moser-Trudinger inequality on $W^{1,n}(M)$". We show how the validity of the Moser-Trudinger inequality can be extended from a local to a global scale under additional assumptions: either by assuming the validity of the Poincar\'e inequality, or by imposing a stronger norm condition. We apply these results to Hadamard manifolds. The technique is general enough to be applicable also in sub-Riemannian settings, such as the Heisenberg group.

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Luigi Fontana, Carlo Morpurgo, Liuyu Qin. 2024-08-13. Moser-Trudinger inequalities: from local to global. https://doi.org/10.1007/s10231-024-01481-9

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