On a multi-particle Moser-Trudinger Inequality

Details On a multi-particle Moser-Trudinger Inequality On a multi-particle Moser-Trudinger Inequality

2004-01-16

arxiv.org/abs/math/0401210v1

Mathematics

Differential Geometry

Scientific paper

We verify a conjecture of Gillet-Soul\'{e}. We prove that the determinant of the Laplacian on a line bundle over $\mathbb{CP}^{1}$ is always bounded from above. This can also be viewed as a multi-particle generalization of the Moser-Trudinger Inequality. Furthermore, we conjecture that this functional achieves its maximum at the canonical metric. We give some evidence for this conjecture, as well as links to other fields of analysis.

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