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arXiv · 1304.0868

Differentiability of Mather's $\beta$-function vs Ma\~n\'e's conjecture

Daniel Massart
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Abstract

We prove that if a time-periodic Tonelli Lagrangian on a closed manifold $M$ satisfies a strong version of the Differentiability Problem for Mather's $\beta$-function, then the Legendre transforms of rational homology classes are dense in the first cohomology of $M$, which is a first step towards Ma\~n\'e's conjecture.

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Daniel Massart. 2013-04-03. Differentiability of Mather's $\beta$-function vs Ma\~n\'e's conjecture. https://arxiv.org/abs/1304.0868

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