@article{BSMF_2000__128_2_151_0, author = {Bordoni, Manlio}, title = {Comparing heat operators through local isometries or fibrations}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {151--178}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {128}, number = {2}, year = {2000}, doi = {10.24033/bsmf.2366}, mrnumber = {2001i:58051}, zbl = {0968.58021}, language = {en}, url = {http://www.numdam.org/articles/10.24033/bsmf.2366/} }
TY - JOUR AU - Bordoni, Manlio TI - Comparing heat operators through local isometries or fibrations JO - Bulletin de la Société Mathématique de France PY - 2000 SP - 151 EP - 178 VL - 128 IS - 2 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/bsmf.2366/ DO - 10.24033/bsmf.2366 LA - en ID - BSMF_2000__128_2_151_0 ER -
%0 Journal Article %A Bordoni, Manlio %T Comparing heat operators through local isometries or fibrations %J Bulletin de la Société Mathématique de France %D 2000 %P 151-178 %V 128 %N 2 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/bsmf.2366/ %R 10.24033/bsmf.2366 %G en %F BSMF_2000__128_2_151_0
Bordoni, Manlio. Comparing heat operators through local isometries or fibrations. Bulletin de la Société Mathématique de France, Tome 128 (2000) no. 2, pp. 151-178. doi : 10.24033/bsmf.2366. http://www.numdam.org/articles/10.24033/bsmf.2366/
[1] Inégalités isopérimétriques pour l'équation de la chaleur et applications à l'estimation de quelques invariants géométriques, in Séminaire Goulaouic-Meyer-Schwarz 1983-1984, exposé n° XV, École Polytechnique, Palaiseau, 1984. | Numdam | Zbl
, . -[2] Laplacians and Riemannian submersions with totally geodesic fibers, Illinois J. Math., t. 26, n° 2, 1982, p. 181-200. | MR | Zbl
, . -[3] Le spectre d'une variété riemannienne, Lecture Notes in Math. 194. - Springer Verlag, Berlin-Heidelberg-New York, 1971. | MR | Zbl
, , . -[4] A Kato type inequality for Riemannian submersions with totally geodesic fibers, Ann. Glob. Analysis and Geometry, t. 4, n° 3, 1986, p. 273-289. | MR | Zbl
. -[5] On symmetrization, Contemporary Mathematics, t. 51, 1986, p. 9-21. | MR | Zbl
. -[6] Geometry of manifolds. - Academic Press, New York-London, 1964. | MR | Zbl
, . -[7] Spectral estimates for Schrödinger and Dirac-type operators on Riemannian manifolds, Math. Ann., t. 298, 1994, p. 693-718. | MR | Zbl
. -[8] Geometric Inequalities, Grundlehren der math. Wiss. 285. - Springer Verlag, 1988. | Zbl
, . -[9] Eigenvalues in Riemannian Geometry. - Academic Press, New York, 1984. | MR | Zbl
. -[10] A lower bound for the heat kernel, Comm. Pure Applied Math., t. 34, 1981, p. 465-480. | MR | Zbl
, . -[11] Estimations du noyau de la chaleur et du noyau de Green d'une variété riemannienne: applications aux variétés privées d'un Ɛ-tube, C.R. Acad. Sci. Paris, t. 303, 1986, p. 135-138. | MR | Zbl
. -[12] Spectre des variétés privées d'un Ɛ-tube, Prépublication Institut Fourier (Grenoble), t. 61, 1986.
. -[13] Spectrum of manifolds with holes, J. Funct. Anal., t. 134, 1995, p. 194-221. | MR | Zbl
. -[14] Heat kernel bounds, conservation of probability and the Feller property, J. Analyse Math., t. 58, 1992, p. 99-119. | MR | Zbl
. -[15] Théorèmes de comparaison en géométrie riemannienne, C.R. Acad. Sci. Paris, t. 281, 1975, p. 455-458. | MR | Zbl
, , . -[16] The conservation property of the heat equation on Riemannian manifolds, Comm. Pure Appl. Math., t. 12, 1959, p. 1-11. | MR | Zbl
. -[17] Inégalités isopérimétriques et analytiques sur les variétés riemanniennes, Astérisque 163-164, 1988, p. 31-91. | Numdam | MR | Zbl
. -[18] Isoperimetric inequalities based on integral norms of Ricci curvature, Astérisque 157-158, 1988, p. 191-216. | Numdam | MR | Zbl
. -[19] Riemannian Geometry. - Universitext, Springer Verlag, New York, 1987. | MR | Zbl
, , . -[20] On stochastically complete manifolds, (in Russian) Dokl. Akad. Nauk. SSSR, t. 290, n° 3, 1986, p. 534-537; English translation in Soviet. Math. Dokl., t. 34, n° 2, 1987, p. 310-313. | MR | Zbl
. -[21] Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds, Preprint, 1997.
. -[22] Kato's inequality and the spectral distribution of Laplacians on compact Riemannian manifolds, J. Diff. Geom., t. 15, 1980, p. 27-38. | MR | Zbl
, , . -[23] Heat semigroup on a complete Riemannian manifold, Ann. Prob., t. 17, 1989, p. 1248-1254. | MR | Zbl
. -[24] Curvature, geodesics and the Brownian motion on a Riemannian manifold, II. Explosion properties, Nagoya Math. J., t. 87, 1982, p. 115-125. | MR | Zbl
. -[25] The heat equation on complete Riemannian manifolds, unpublished.
, . -[26] A mean-value lemma and applications to heat diffusion, Prépublication Institut Fourier (Grenoble), t. 327, 1996.
. -[27] Algebraic Topology. - McGraw-Hill, New York, 1966. | MR | Zbl
. -[28] Analysis on local Dirichlet spaces I. Recurrence, conservativeness and Lp-Liouville properties, J. reine angew. Math., t. 456, 1994, p. 173-196. | MR | Zbl
. -[29] On a martingale method for symmetric diffusion process and its applications, Osaka J. Math., t. 26, 1989, p. 605-623. | MR | Zbl
. -[30] Eigenvalues estimates with applications to minimal surfaces, Pacific J. Math., t. 128, 1987, p. 361-366. | MR | Zbl
. -[31] Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana Math. J., t. 25, 1976, p. 659-670. | MR | Zbl
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