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An integral equation in conformal geometry |
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| Authors: | Fengbo Hang Xiaodong Wang Xiaodong Yan |
| Affiliation: | 1. Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA;2. Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA |
| Abstract: | Motivated by Carleman's proof of the isoperimetric inequality in the plane, we study the problem of finding a metric with zero scalar curvature maximizing the isoperimetric ratio among all zero scalar curvature metrics in a fixed conformal class on a compact manifold with boundary. We derive a criterion for the existence and make a related conjecture. |
| Keywords: | Isoperimetric inequalities Poisson kernel Yamabe type integral equations |
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