Moser-Trudinger inequality on conformal discs

Mathematics – Analysis of PDEs

Scientific paper

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Scientific paper

We show that the Moser-Trudinger inequality holds in a conformal disc if and
only if the metric is bounded from above by the Hyperbolic metric. We also find
a necessary and sufficient condition for the Moser-Trudinger inequality to hold
in an unbounded subset of the two dimensional Euclidean space.

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