On a multi-particle Moser-Trudinger Inequality

Hao Fang

doi:10.4310/CAG.2004.v12.n5.a8

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On a multi-particle Moser-Trudinger Inequality

Journal article

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On a multi-particle Moser-Trudinger Inequality

Hao Fang

Communications in analysis and geometry, Vol.12(5), pp.1155-1172

01/16/2004

DOI: 10.4310/CAG.2004.v12.n5.a8

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Abstract

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.

Details

Title: Subtitle: On a multi-particle Moser-Trudinger Inequality
Creators: Hao Fang - CIMS, Nyu
Resource Type: Journal article
Publication Details: Communications in analysis and geometry, Vol.12(5), pp.1155-1172
DOI: 10.4310/CAG.2004.v12.n5.a8
ISSN: 1019-8385
eISSN: 1944-9992
Language: English
Date published: 01/16/2004
Academic Unit: Mathematics
Record Identifier: 9984242358802771

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