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Upper Bounds for Regularized Determinants |
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| Authors: | H. Gillet C. Soulé |
| Affiliation: | (1) Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 60607-7045, USA, US;(2) CNRS, Institut des Hautes études Scientifiques, 35, Route de Chartres, 91440, Bures-sur-Yvette, France, FR |
| Abstract: | We conjecture that the zeta-regularized determinant of the Laplace operator with coefficients in a holomorphic vector bundle on a compact K?hler manifold remains bounded when the metric on the bundle varies. This conjecture is shown to be true for certain classes of line bundles on Riemann surfaces. Received: 7 July 1997 / Accepted: 20 April 1998 |
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