Moser-Trudinger inequalities on 2-dimensional Hadamard manifolds

Abstract

We derive two types of sharp Moser-Trudinger inequalities on complete, simply connected, two-dimensional Riemannian manifolds whose sectional curvatures $ K $ satisfy the bounds $ -b^2\le K\le -a^2 < 0 $.

Keywords

• moser-trudinger inequalities
• hadamard manifolds