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Isoperimetric inequalities for Riemannian products

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Literature cited

  1. 1.

    A. K. Guschin, “Estimates: of solutions of boundary problems for parabolic second-order equations,” Tr. MIAN SSSR,126, 5–45 (1973).

  2. 2.

    V. V. Minakhin, “Liouville's theorem and the Harnack inequality for Beltrami's equation on an arbitrary manifold,” Funkts. Anal. Prilozhen.,14, No. 2, 71–72 (1980).

  3. 3.

    S. Y. Cheng, P. Li, and S. T. Yau, “On the upper estimate of the heat kernel of a complete Riemannian manifold,” Am. J. Math.,105, No. 5, 1021–1063 (1981).

  4. 4.

    A. A. Grigor'yan, “A Liouville theorem on a Riemannian manifold,” Tr. Tbilisskogo Univ., Ser. Mat., Mekh., Astron.,232-233, No. 13–14, 49–76 (1982).

  5. 5.

    A. A. Grigor'yan, “Existence of a Green's function on a manifold,” Usp. Mat. Nauk,38, No. 1, 161–162 (1983).

  6. 6.

    S. T. Yau, “Isoperimetric constant and the first eigenvalue of a compact Riemannian manifold,” Ann. Sci. Ecole Norm. Sup., Ser. IV,8, No. 4, 487–507 (1975).

  7. 7.

    D. Hoffman and J. Spruck, “Sobolev and isoperimetric inequalities for Riemannian sub-manifolds,” Commun. Pure Appl. Math.,27, No. 6, 715–727 (1974).

  8. 8.

    W. Mazja, Einbettungssätze für Sobolewsche Räume, Vol. 1, Teubner, Leipzig (1979).

  9. 9.

    A. A. Grigor'yan, “Harmonically degenerate manifolds,” Usp. Mat. Nauk,37, No. 4, 106 (1982).

  10. 10.

    H. Federer, Geometric Measure Theory, Springer-Verlag, Berlin (1969).

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Translated from Matematicheskie Zametki, Vol. 38, No. 4, pp. 617–626, October, 1985.

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Grigor'yan, A.A. Isoperimetric inequalities for Riemannian products. Mathematical Notes of the Academy of Sciences of the USSR 38, 849–854 (1985). https://doi.org/10.1007/BF01158414

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Keywords

  • Isoperimetric Inequality
  • Riemannian Product