Skip to main content Accesibility Help
×
×
Home

Determinant of the Laplacian on Tori of Constant Positive Curvature with one Conical Point

  • Victor Kalvin (a1) and Alexey Kokotov (a1)
Abstract

We find an explicit expression for the zeta-regularized determinant of (the Friedrichs extensions of) the Laplacians on a compact Riemann surface of genus one with conformal metric of curvature $1$ having a single conical singularity of angle $4\unicode[STIX]{x1D70B}$ .

Copyright
References
Hide All
[1] Chai, C.-L., Lin, C.-S., and Wang, C.-L., Mean field equation, hyperelliptic curves and modular forms: I . Camb. J. Math. 3(2015), no. 1–2, 127274. https://doi.org/10.4310/CJM.2015.v3.n1.a3.
[2] Clemens, C. H., A scrapbook of complex curve theory. Second ed., Graduate Studies in Mathematics, 55, American Mathematical Society, Providence, RI, 2003.
[3] Eremenko, A., Metrics of positive curvature with conic singularities on the sphere . Proc. Amer. Math. Soc. 132(2004), no. 11, 33493355. https://doi.org/10.1090/S0002-9939-04-07439-8.
[4] Kalvin, V., On determinants of Laplacians on compact Riemann surfaces equipped with pullbacks of conical metrics by meromorphic functions . J. Geom. Anal., to appear. https://doi.org/10.1007/s12220-018-0018-2.
[5] Kalvin, V. and Kokotov, A., Metrics of constant positive curvature, Hurwitz spaces and det Δ . Int. Math. Res. Not. IMRN, to appear. https://doi.org/10.1093/imrn/rnx224.
[6] Kitaev, V. and Korotkin, D., On solutions of the Schlesinger equations in terms of theta-functions . Int. Math. Res. Not. IMRN 1998 no. 17, 877905. https://doi.org/10.1155/S1073792898000543.
[7] Kokotov, A. and Korotkin, D., Tau-functions on Hurwitz spaces . Math. Phys. Anal. Geom. 7(2004), no. 1, 4796. https://doi.org/10.1023/B:MPAG.0000022835.68838.56.
[8] Kokotov, A. and Korotkin, D., Isomonodromic tau-function of Hurwitz Frobenius manifolds . Int. Math. Res. Not. IMRN 2006, Art. ID 18746. https://doi.org/10.1155/IMRN/2006/18746.
[9] Kokotov, A. and Strachan, I., On the isomonodromic tau-function for the Hurwitz spaces of branched coverings of genus zero and one . Math. Res. Lett. 12(2005), no. 5–6, 857875. https://doi.org/10.4310/MRL.2005.v12.n6.a7.
[10] Polchinski, J., Evaluation of the one loop string path integral . Comm. Math. Phys. 104(1986), no. 1, 3747.
[11] Ray, D. B. and Singer, I. M., Analytic torsion for complex manifolds . Ann. of Math. 98(1973), 154177. https://doi.org/10.2307/1970909.
[12] Sarnak, P., Some applications of modular forms. Cambridge Tracts in Mathematics, 99, Cambridge University Press, 1990. https://doi.org/10.1017/CBO9780511895593.
[13] Umehara, M. and Yamada, K., Metrics of constant curvature 1 with three conical singularities on 2-sphere . Illinois J. Math. 44(2000), no. 1, 7294.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed