Genus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of Laplacians

Details Genus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of Laplacians Genus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of Laplacians

2006-05-23

arxiv.org/abs/math/0605614v2

Mathematics

Differential Geometry

18 pages

Scientific paper

We prove a formula for the determinant of Laplacian on an arbitrary compact polyhedral surface of genus one. This formula generalizes the well-known Ray-Singer result for a flat torus. A special case of flat conical metrics given by the modulus of a meromorphic quadratic differential on an elliptic surface is also considered. We study the determinant of Laplacian as a functional on the moduli space of meromorphic quadratic differentials with L simple poles and L simple zeros and derive formulas for variations of this functional w. r. t. natural coordinates on this moduli space. A new proof of the Troyanov theorem about flat conical metrics on compact Riemann surfaces of arbitrary genus is also given.

Affiliated with

Also associated with

No associations

Rating

Genus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of Laplacians does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Genus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of Laplacians, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Genus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of Laplacians will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-182118