Comparing heat operators through local isometries or fibrations

Manlio Bordoni

Bulletin de la Société Mathématique de France (2000)

  • Volume: 128, Issue: 2, page 151-178
  • ISSN: 0037-9484

How to cite

top

Bordoni, Manlio. "Comparing heat operators through local isometries or fibrations." Bulletin de la Société Mathématique de France 128.2 (2000): 151-178. <http://eudml.org/doc/87824>.

@article{Bordoni2000,
author = {Bordoni, Manlio},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Riemannian coverings; heat kernel; local isometry; capacity; Kato's inequality; Riemannian submersions},
language = {eng},
number = {2},
pages = {151-178},
publisher = {Société mathématique de France},
title = {Comparing heat operators through local isometries or fibrations},
url = {http://eudml.org/doc/87824},
volume = {128},
year = {2000},
}

TY - JOUR
AU - Bordoni, Manlio
TI - Comparing heat operators through local isometries or fibrations
JO - Bulletin de la Société Mathématique de France
PY - 2000
PB - Société mathématique de France
VL - 128
IS - 2
SP - 151
EP - 178
LA - eng
KW - Riemannian coverings; heat kernel; local isometry; capacity; Kato's inequality; Riemannian submersions
UR - http://eudml.org/doc/87824
ER -

References

top
  1. [1] BÉRARD (P.), GALLOT (S.). — 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. Zbl0542.53025
  2. [2] BÉRARD BERGERY (L.), BOURGUIGNON (J.P.). — Laplacians and Riemannian submersions with totally geodesic fibers, Illinois J. Math., t. 26, n° 2, 1982, p. 181-200. Zbl0483.58021MR84m:58153
  3. [3] BERGER (M.), GAUDUCHON (P.), MAZET (E.). — Le spectre d'une variété riemannienne, Lecture Notes in Math. 194. — Springer Verlag, Berlin-Heidelberg-New York, 1971. Zbl0223.53034MR43 #8025
  4. [4] BESSON (G.). — A Kato type inequality for Riemannian submersions with totally geodesic fibers, Ann. Glob. Analysis and Geometry, t. 4, n° 3, 1986, p. 273-289. Zbl0631.53035MR89b:58215
  5. [5] BESSON (G.). — On symmetrization, Contemporary Mathematics, t. 51, 1986, p. 9-21. Zbl0589.53049MR87m:58161
  6. [6] BISHOP (R.L.), CRITTENDEN (R.J.). — Geometry of manifolds. — Academic Press, New York-London, 1964. Zbl0132.16003MR29 #6401
  7. [7] BORDONI (M.). — Spectral estimates for Schrödinger and Dirac-type operators on Riemannian manifolds, Math. Ann., t. 298, 1994, p. 693-718. Zbl0791.58094MR95i:58179
  8. [8] BURAGO (Yu.D.), ZALGALLER (V.A.). — Geometric Inequalities, Grundlehren der math. Wiss. 285. — Springer Verlag, 1988. Zbl0633.53002
  9. [9] CHAVEL (I.). — Eigenvalues in Riemannian Geometry. — Academic Press, New York, 1984. Zbl0551.53001MR86g:58140
  10. [10] CHEEGER (J.), YAU (S.T.). — A lower bound for the heat kernel, Comm. Pure Applied Math., t. 34, 1981, p. 465-480. Zbl0481.35003MR82i:58065
  11. [11] COURTOIS (G.). — 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. Zbl0588.53030MR87h:58220
  12. [12] COURTOIS (G.). — Spectre des variétés privées d'un Ɛ-tube, Prépublication Institut Fourier (Grenoble), t. 61, 1986. 
  13. [13] COURTOIS (G.). — Spectrum of manifolds with holes, J. Funct. Anal., t. 134, 1995, p. 194-221. Zbl0847.58076MR97b:58142
  14. [14] DAVIES (E.B.). — Heat kernel bounds, conservation of probability and the Feller property, J. Analyse Math., t. 58, 1992, p. 99-119. Zbl0808.58041MR94e:58136
  15. [15] DEBIARD (A.), GAVEAU (B.), MAZET (E.). — Théorèmes de comparaison en géométrie riemannienne, C.R. Acad. Sci. Paris, t. 281, 1975, p. 455-458. Zbl0327.58014MR55 #4294
  16. [16] GAFFNEY (M.P.). — The conservation property of the heat equation on Riemannian manifolds, Comm. Pure Appl. Math., t. 12, 1959, p. 1-11. Zbl0102.09202MR21 #892
  17. [17] GALLOT (S.). — Inégalités isopérimétriques et analytiques sur les variétés riemanniennes, Astérisque 163-164, 1988, p. 31-91. Zbl0674.53001MR90f:58173
  18. [18] GALLOT (S.). — Isoperimetric inequalities based on integral norms of Ricci curvature, Astérisque 157-158, 1988, p. 191-216. Zbl0665.53041MR90a:58179
  19. [19] GALLOT (S.), HULIN (D.), LAFONTAINE (J.). — Riemannian Geometry. — Universitext, Springer Verlag, New York, 1987. Zbl0636.53001MR88k:53001
  20. [20] GRIGOR'YAN (A.). — 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. Zbl0632.58041MR88a:58209
  21. [21] GRIGOR'YAN (A.). — Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds, Preprint, 1997. 
  22. [22] HESS (H.), SCHRADER (R.), UHLENBROCK (D.A.). — Kato's inequality and the spectral distribution of Laplacians on compact Riemannian manifolds, J. Diff. Geom., t. 15, 1980, p. 27-38. Zbl0442.58032MR82g:58090
  23. [23] HSU (P.). — Heat semigroup on a complete Riemannian manifold, Ann. Prob., t. 17, 1989, p. 1248-1254. Zbl0694.58043MR90j:58158
  24. [24] ICHIHARA (K.). — Curvature, geodesics and the Brownian motion on a Riemannian manifold, II. Explosion properties, Nagoya Math. J., t. 87, 1982, p. 115-125. Zbl0514.58039MR84m:58166b
  25. [25] KARP (P.), LI (P.). — The heat equation on complete Riemannian manifolds, unpublished. 
  26. [26] SAVO (A.). — A mean-value lemma and applications to heat diffusion, Prépublication Institut Fourier (Grenoble), t. 327, 1996. 
  27. [27] SPANIER (E.H.). — Algebraic Topology. — McGraw-Hill, New York, 1966. Zbl0145.43303MR35 #1007
  28. [28] STURM (K.-T.). — Analysis on local Dirichlet spaces I. Recurrence, conservativeness and Lp-Liouville properties, J. reine angew. Math., t. 456, 1994, p. 173-196. Zbl0806.53041MR95i:31003
  29. [29] TAKEDA (M.). — On a martingale method for symmetric diffusion process and its applications, Osaka J. Math., t. 26, 1989, p. 605-623. Zbl0717.60090MR91d:60193
  30. [30] TISK (J.). — Eigenvalues estimates with applications to minimal surfaces, Pacific J. Math., t. 128, 1987, p. 361-366. Zbl0594.58018MR88i:53102
  31. [31] YAU (S.T.). — Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana Math. J., t. 25, 1976, p. 659-670. Zbl0335.53041MR54 #5502

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.