Skip to main content
SpringerLink
Log in

Heat Content Asymptotics for Oblique Boundary Conditions

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

We consider the short-time heat content asymptotics for oblique boundary conditions. The first few coefficients in the asymptotic expansion are calculated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Avramidi, I. G. and Esposito, G.: New invariants in the one-loop divergences on manifolds with boundary, Classical Quantum Gravity 15 (1998), 281–297.

    Google Scholar 

  2. Avramidi, I. G. and Esposito, G.: Gauge theories on manifolds with boundary, Comm. Math. Phys. 200 (1999), 495–543.

    Google Scholar 

  3. Van den Berg, M., Desjardins, S. and Gilkey, P. B.: Functorality and heat content asymptotics for operators of Laplace type, Topol. Methods Nonlinear Anal. 2 (1993), 147–162.

    Google Scholar 

  4. Van den Berg, M. and Gilkey, P. B.: Heat content asymptotics of a Riemannian manifold with boundary, J. Funct. Anal. 120 (1994), 48–71.

    Google Scholar 

  5. Desjardins, S. and Gilkey, P. B.: Heat content asymptotics for operators of Laplace type with Neumann boundary conditions, Math. Z. 215 (1994), 251–268.

    Google Scholar 

  6. Dowker, J. S. and Kirsten, K.: Heat-kernel coefficients for oblique boundary conditions, Classical Quantum Gravity 14 (1997), L169–L175.

    Google Scholar 

  7. Dowker, J. S. and Kirsten, K.: The a(3/2) heat kernel coefficient for oblique boundary conditions, Classical Quantum Gravity 16 (1999), 1917–1936.

    Google Scholar 

  8. Egorov, Yu. V. and Shubin, M. A.: Partial-Differential Equations, Springer-Verlag, Berlin, 1991.

    Google Scholar 

  9. Gilkey, P. B.: Invariance Theory, the Heat Equation and the Atiyah-Singer Index Theorem, CRC Press, Boca Raton, 1995.

    Google Scholar 

  10. Gilkey, P. B. and Park, J H.: Heat content asymptotics, In: Quantum Gravity and Spectral Geometry, Nuclear Phys. B Proc. Suppl. 104 (2002), 185–188.

    Google Scholar 

  11. Krantz, S. G.: Partial Differential Equations and Complex Analysis, CRC Press, Boca Raton, 1992.

    Google Scholar 

  12. McAvity, D. M.: Heat kernel asymptotics for mixed boundary conditions, Classical Quantum Gravity 9 (1992), 1983–1998.

    Google Scholar 

  13. McAvity, D. M.: Surface energy from heat content asymptotics, J. Phys. A: Math. Gen. 26 (1993), 823–830.

    Google Scholar 

  14. Treves, F.: Introduction to Pseudodifferential and Fourier Integral Operators, Vol. 1. Plenum, New York, 1980.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, University of Oregon, Eugene, OR, 97403, U.S.A.

    Peter Gilkey

  2. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22–26, 04103, Leipzig, Germany

    Klaus Kirsten

  3. Mathematics Department, Honam University, Seobongdong 59, Kwang-sanku, Kwangju, 506-090, South Korea

    Jeonghyeong Park

Authors
  1. Peter Gilkey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Klaus Kirsten
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jeonghyeong Park
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gilkey, P., Kirsten, K. & Park, J. Heat Content Asymptotics for Oblique Boundary Conditions. Letters in Mathematical Physics 59, 269–276 (2002). https://doi.org/10.1023/A:1015521817393

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015521817393

Search

Navigation