×

zbMATH — the first resource for mathematics

Determinants of Cauchy-Riemann operators on a Riemann surface. (English. Russian original) Zbl 0603.32016
Funct. Anal. Appl. 19, 31-34 (1985); translation from Funkts. Anal. Prilozh. 19, No. 1, 37-41 (1985).
The author considers on a smooth vector bundle over a compact Riemann surface the space of \(\overline{\partial}\) operators (corresponding to the possible complex structures) and constructs on this space a determinant by using the concepts of a determinant line bundle and the determinant of an elliptic operator.

MSC:
32F99 Geometric convexity in several complex variables
58J99 Partial differential equations on manifolds; differential operators
30F10 Compact Riemann surfaces and uniformization
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] D. Ray and I. Singer, ”Analytic torsion,” Ann. Math.,98, No. 1, 154-177 (1973). · Zbl 0267.32014 · doi:10.2307/1970909
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.