Determinant of the Neumann operator on smooth Jordan curves
Authors:
Julian Edward and Siye Wu
Journal:
Proc. Amer. Math. Soc. 111 (1991), 357-363
MSC:
Primary 58G11; Secondary 35S99, 58G15, 58G20
DOI:
https://doi.org/10.1090/S0002-9939-1991-1031662-0
MathSciNet review:
1031662
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Abstract | References | Similar Articles | Additional Information
Abstract: Using the method of heat kernel expansion, the determinant of the Neumann operator on an arbitrary smooth Jordan curve is shown to be equal to the circumference.
- [1] Jeff Cheeger, Analytic torsion and the heat equation, Ann. of Math. (2) 109 (1979), no. 2, 259–322. MR 528965, https://doi.org/10.2307/1971113
- [2] Eric D’Hoker and D. H. Phong, On determinants of Laplacians on Riemann surfaces, Comm. Math. Phys. 104 (1986), no. 4, 537–545. MR 841668
- [3] S. W. Hawking, Zeta function regularization of path integrals in curved spacetime, Comm. Math. Phys. 55 (1977), no. 2, 133–148. MR 524257
- [4] B. Osgood, R. Phillips, and P. Sarnak, Extremals of determinants of Laplacians, J. Funct. Anal. 80 (1988), no. 1, 148–211. MR 960228, https://doi.org/10.1016/0022-1236(88)90070-5
- [5] D. B. Ray and I. M. Singer, 𝑅-torsion and the Laplacian on Riemannian manifolds, Advances in Math. 7 (1971), 145–210. MR 295381, https://doi.org/10.1016/0001-8708(71)90045-4
- [6] D. B. Ray and I. M. Singer, Analytic torsion for complex manifolds, Ann. of Math. (2) 98 (1973), 154–177. MR 383463, https://doi.org/10.2307/1970909
- [7] Steven Rosenberg, The variation of the de Rham zeta function, Trans. Amer. Math. Soc. 299 (1987), no. 2, 535–557. MR 869220, https://doi.org/10.1090/S0002-9947-1987-0869220-4
- [8] R. T. Seeley, Complex powers of an elliptic operator, Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966) Amer. Math. Soc., Providence, R.I., 1967, pp. 288–307. MR 0237943
- [9] Scott A. Wolpert, Asymptotics of the spectrum and the Selberg zeta function on the space of Riemann surfaces, Comm. Math. Phys. 112 (1987), no. 2, 283–315. MR 905169
-torsion and the Laplacian on Riemannian manifolds, Adv. in Math. 7 (1971), 145-210. Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58G11, 35S99, 58G15, 58G20
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1991-1031662-0
Keywords:
Zeta function,
determinant,
heat kernel
Article copyright:
© Copyright 1991
American Mathematical Society
