Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

THE SPECTRAL GEOMETRY OF EINSTEIN MANIFOLDS WITH BOUNDARY

  • Published : 2004.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

Let (M,g) be a compact m dimensional Einstein manifold with smooth boundary. Let $\Delta$$_{p}$,B be the realization of the p form valued Laplacian with a suitable boundary condition B. Let Spec($\Delta$$_{p}$,B) be the spectrum where each eigenvalue is repeated according to multiplicity. We show that certain geometric properties of the boundary may be spectrally characterized in terms of this data where we fix the Einstein constant.ant.

Keywords

References

  1. T. Branson and P. Gilkey, The asymptotics of the Laplacian on a manifold with boundary, Comm. Partial Differential Equations 15 (1990), 245–272 https://doi.org/10.1080/03605309908820686
  2. P. B. Gilkey, Asymptotic Formulae in Spectral Geometry, CRC Press, 2003
  3. V. K. Patodi, Curvature and the fundamental solution of the heat operator, J. Indian Math. Soc. 34 (1970), 269–285
  4. J. H. Park, Spectral geometry and the Kaehler condition for He rmitian manifolds with boundary, Contemp. Math. 337 (2003) AMS, 121–128
  5. R. T. Seeley, Complex powers of an elliptic operator, Proc. Sympos. Pure Math. 10 (1968), 288–307
  6. R. T. Seeley, Analytic extension of the trace associated with elliptic boundary problems, Amer. J. Math. 91 (1969), 963–983 https://doi.org/10.2307/2373312

Cited by

  1. Spectral geometry of eta-Einstein Sasakian manifolds vol.62, pp.11, 2012, https://doi.org/10.1016/j.geomphys.2012.06.007
  2. Multi- C ∗ $C^{*}$ -ternary algebras and applications vol.2015, pp.1, 2015, https://doi.org/10.1186/s13660-015-0746-9
  3. On the stability of ∗-derivations on Banach ∗-algebras vol.2012, pp.1, 2012, https://doi.org/10.1186/1687-1847-2012-138