Kodai Mathematical Journal

The fundamental solutions of the heat equations on Riemannian spaces with cone-like singular points

Masayoshi Nagase

Full-text: Open access

Article information

Source
Kodai Math. J. Volume 7, Number 3 (1984), 382-455.

Dates
First available: 23 January 2006

Permanent link to this document
http://projecteuclid.org/euclid.kmj/1138036957

Mathematical Reviews number (MathSciNet)
MR0760044

Zentralblatt MATH identifier
0599.58043

Digital Object Identifier
doi:10.2996/kmj/1138036957

Subjects
Primary: 58G11
Secondary: 58G25

Citation

Nagase, Masayoshi. The fundamental solutions of the heat equations on Riemannian spaces with cone-like singular points. Kodai Mathematical Journal 7 (1984), no. 3, 382--455. doi:10.2996/kmj/1138036957. http://projecteuclid.org/euclid.kmj/1138036957.


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References

  • [1] J. CHEEGER, Analytic torsion and the heat equation, Ann. Math., 109 (1979), 259-322.
  • [2] J. CHEEGER, On the spectral geometry of spaces with cone-like singularities, P. N. A. S., V. 76, No.5, (1979), 2103-2106.
  • [3] J. CHEEGER, Spectral geometry of spaces with cone-like singularities, preprint, (1978).
  • [4] J. CHEEGER, On the Hodge theory of Riemannian pseudomanifolds, Proc. Sym. Pure Math., 36 (1980), 91-146.
  • [5] J. CHEEGER, M. GORESKY AND R. MACPERSON, Zcohomology and intersection homology of singular algebraic varieties, in Proceeding of year in differential geometry, LA. S., S. Yau ed. (1981), Ann. Math. Studies, Princeton.
  • [6] J. CHEEGER AND M. TAYLOR, On the diffraction of waves byconical singularities I, II, Comm. Pure Appl. Math., XXXV (1982), 275-331: XXXV (1982), 487-529.
  • [7] P. E. CONNER, The Neumann's problem for differential forms on Riemannian manifolds, Mem. Amer. Math. Soc, 20 (1956).
  • [8] J. DUISTERMAAT AND V. GuiLLEMiN, Thespectrum of positive elliptic operators and periodic ^characteristics, Invent. Math., 20 (1975), 39-79.
  • [9] M. P. GAFFNEY, A special Stokes theorem for Riemannian manifolds, Ann. Math., V. 60, No. 1, (1954), 140-145.
  • [10] M. P. GAFFNEY, Theheat equation method of Milgram and Rosenbloom for open Riemannian manifolds, Ann. Math., V. 60, No. 3, (1954), 458-466.
  • [11] P. GREINER, An asymptotic expansion for the heat equation, Arch. Rat. Mech. Anal., 41 (1971), 163-218.
  • [12] V. GUILLEMIN AND S. STERNBERG, Geometric Asymptotics, A. M. S., Math. Surveys, No. 14 (1977).
  • [13] L. HORMNDER, Thespectral function of an elliptic operator, Acta. Math., 121 (1968), 193-218.
  • [14] S. MORIGUTI, K. UDAGAWA AND S. HITOTUMATU, Sgaku Kshiki I, II, III, Iwanami Shoten (in Japanese).
  • [15] M. NAGASE, DeRham-Hodge theory on a manifold with cone-like singularities, Kodai Math. J., V. 5, No. 1, (1982), 38-64.
  • [16] M. NAGASE, Zcohomology andintersection homology of stratified spaces, Duke Math. J., V. 50, No. 1, (1983), 329-368.
  • [17] D. B. RAY AND I. M. SINGER, i?-torsion and the Laplacian on Riemannian manifolds, Adv. in Math., 7 (1971), 145-210.
  • [18] M. TAYLOR, Pseudodifferential Operators, Princeton Univ. Press, (1981).