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arXiv · 1501.07470

A Trudinger-Moser inequality on compact Riemannian surface involving Gaussian curvature

Yunyan Yang
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Abstract

Motivated by a recent work of X. Chen and M. Zhu (Commun. Math. Stat., 1 (2013) 369-385), we establish a Trudinger-Moser inequality on compact Riemannian surface without boundary. The proof is based on blow-up analysis together with Carleson-Chang's result (Bull. Sci. Math. 110 (1986) 113-127). This inequality is different from the classical one, which is due to L. Fontana (Comment. Math. Helv., 68 (1993) 415-454), since the Gaussian curvature is involved. As an application, we improve Chen-Zhu's result as follows: A modified Liouville energy of conformal Riemannian metric has a uniform lower bound, provided that the Euler characteristic is nonzero and the volume of the conformal surface has a uniform positive lower bound.

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Yunyan Yang. 2015-01-29. A Trudinger-Moser inequality on compact Riemannian surface involving Gaussian curvature. https://arxiv.org/abs/1501.07470

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