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Mat. Sb., 1991, Volume 182, Number 1, Pages 55–87 (Mi msb1274)  

This article is cited in 60 scientific papers (total in 60 papers)

The heat equation on noncompact Riemannian manifolds

A. A. Grigor'yan


Abstract: The behavior of the Green function $G(x,y,t)$ of the Cauchy problem for the heat equation on a connected, noncompact, complete Riemannian manifold is investigated. For manifolds with boundary it is assumed that the Green function satisfies a Neumann condition on the boundary.

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English version:
Mathematics of the USSR-Sbornik, 1992, 72:1, 47–77

Bibliographic databases:

UDC: 517.9
MSC: 58G11
Received: 07.07.1988 and 15.08.1990

Citation: A. A. Grigor'yan, “The heat equation on noncompact Riemannian manifolds”, Mat. Sb., 182:1 (1991), 55–87; Math. USSR-Sb., 72:1 (1992), 47–77

Citation in format AMSBIB
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\by A.~A.~Grigor'yan
\paper The heat equation on noncompact Riemannian manifolds
\jour Mat. Sb.
\yr 1991
\vol 182
\issue 1
\pages 55--87
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\transl
\jour Math. USSR-Sb.
\yr 1992
\vol 72
\issue 1
\pages 47--77
\crossref{https://doi.org/10.1070/SM1992v072n01ABEH001410}
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    1. V. G. Tkachev, “A sharp lower bound for the first eigenvalue on a minimal surface”, Math. Notes, 54:2 (1993), 835–840  mathnet  crossref  mathscinet  zmath  isi
    2. Li P. Tam L., “Greens-Functions, Harmonic-Functions, and Volume Comparison”, J. Differ. Geom., 41:2 (1995), 277–318  mathscinet  zmath  isi
    3. Benjamini I., Chavel I., Feldman E., “Heat Kernel Lower Bounds on Riemannian Manifolds Using the Old Ideas of Nash”, Proc. London Math. Soc., 72:1 (1996), 215–240  crossref  mathscinet  zmath  isi
    4. Qi S. Zhang, “A New Critical Phenomenon for Semilinear Parabolic Problems”, Journal of Mathematical Analysis and Applications, 219:1 (1998), 125  crossref
    5. Hajlasz P., Strzelecki P., “Subelliptic P-Harmonic Maps Into Spheres and the Ghost of Hardy Spaces”, Math. Ann., 312:2 (1998), 341–362  crossref  mathscinet  zmath  isi
    6. Sung C., “A Note on the Existence of Positive Green's Function”, J. Funct. Anal., 156:1 (1998), 199–207  crossref  mathscinet  zmath  isi
    7. Coulhon T., Grigoryan A., “Random Walks on Graphs with Regular Volume Growth”, Geom. Funct. Anal., 8:4 (1998), 656–701  crossref  mathscinet  zmath  isi
    8. Li P., Wang J., “Mean Value Inequalities”, Indiana Univ. Math. J., 48:4 (1999), 1257–1283  mathscinet  zmath  isi
    9. Grigor'yan A. Saloff-Coste L., “Heat Kernel on Connected Sums of Riemannian Manifolds”, Math. Res. Lett., 6:3-4 (1999), 307–321  mathscinet  isi
    10. Zhang Q., “Blow-Up Results for Nonlinear Parabolic Equations on Manifolds”, Duke Math. J., 97:3 (1999), 515–539  crossref  mathscinet  zmath  isi
    11. Grigor'yan A., “Analytic and Geometric Background of Recurrence and Non-Explosion of the Brownian Motion on Riemannian Manifolds”, Bull. Amer. Math. Soc., 36:2 (1999), 135–249  crossref  mathscinet  isi
    12. Holopainen I., “Volume Growth, Green's Functions, and Parabolicity of Ends”, Duke Math. J., 97:2 (1999), 319–346  crossref  mathscinet  zmath  adsnasa  isi
    13. Hambly B., Kumagai T., “Transition Density Estimates for Diffusion Processes on Post Critically Finite Self-Similar Fractals”, Proc. London Math. Soc., 78:2 (1999), 431–458  crossref  mathscinet  zmath  isi
    14. Martin T. Barlow, Richard F. Bass, “Divergence Form Operators on Fractal-like Domains”, Journal of Functional Analysis, 175:1 (2000), 214  crossref
    15. Hajlasz P., Koskela P., “Sobolev Met Poincaré”, Mem. Am. Math. Soc., 145:688 (2000), IX+  mathscinet  isi
    16. Grigor'yan A., “Heat Kernels on Manifolds, Graphs and Fractals”, European Congress of Mathematics, Vol I, Progress in Mathematics, 201, eds. Casacuberta C., MiroRoig R., Verdera J., XamboDescamps S., Birkhauser Verlag Ag, 2001, 393–406  mathscinet  isi
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    22. Thierry Coulhon, Xuan Thinh Duong, “Riesz transform and related inequalities on non-compact Riemannian manifolds”, Comm Pure Appl Math, 56:12 (2003), 1728  crossref  mathscinet  zmath  isi
    23. Coulhon T. Grigor'yan A. Levin D., “On Isoperimetric Profiles of Product Spaces”, Commun. Anal. Geom., 11:1 (2003), 85–120  mathscinet  zmath  isi
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    25. Auscher P., Coulhon T., Duong X., Hofmann S., “Riesz Transform on Manifolds and Heat Kernel Regularity”, Ann. Sci. Ec. Norm. Super., 37:6 (2004), 911–957  crossref  mathscinet  zmath  isi
    26. Kumagai T., “Heat Kernel Estimates and Parabolic Harnack Inequalities on Graphs and Resistance Forms”, Publ. Res. Inst. Math. Sci., 40:3 (2004), 793–818  crossref  mathscinet  zmath  isi
    27. Kim S., “Harnack Inequality for Nondivergent Elliptic Operators on Riemannian Manifolds”, Pac. J. Math., 213:2 (2004), 281–293  crossref  mathscinet  zmath  isi
    28. C. M. P. A. Smulders, “Heat Kernels on homogeneous spaces”, J Austral Math Soc, 78:1 (2005), 109  crossref  mathscinet  zmath  isi
    29. M. van den Berg, “Heat content and Hardy inequality for complete Riemannian manifolds”, Journal of Functional Analysis, 233:2 (2006), 478  crossref
    30. Telcs A., “Sub-Gaussian Short Time Asymptotics for Measure Metric Dirichlet Spaces”, J. Theor. Probab., 19:3 (2006), 631–645  crossref  mathscinet  zmath  isi
    31. Kim P., Song R., “Two-Sided Estimates on the Density of Brownian Motion with Singular Drift”, Ill. J. Math., 50:3 (2006), 635–688  mathscinet  zmath  isi
    32. [Anonymous], “Non-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Caratheodory Spaces - Introduction”, Mem. Am. Math. Soc., 182:857 (2006), 1+  mathscinet  isi
    33. Zhang Q.S., “Stability of the Cheng-Yau Gradient Estimate”, Pac. J. Math., 225:2 (2006), 379–398  crossref  mathscinet  zmath  isi
    34. Mustapha S., “Gaussian Estimates for Spatially Inhomogeneous Random Walks on Z(D)”, Ann. Probab., 34:1 (2006), 264–283  crossref  mathscinet  zmath  isi
    35. Grigor'yan A., “Heat Kernels on Weighted Manifolds and Applications”, Ubiquitous Heat Kernel, Contemporary Mathematics Series, 398, ed. Jorgenson J. Walling L., Amer Mathematical Soc, 2006, 93–191  crossref  mathscinet  isi
    36. V. Knopova, “A Note on the Transition Density Estimate for Some Diffusion Process on a d–Set”, Acta Appl Math, 96:1-3 (2007), 293  crossref  mathscinet  zmath  isi
    37. Kassmann M., “Harnack Inequalities: an Introduction”, Bound. Value Probl., 2007, 81415  crossref  mathscinet  zmath  isi
    38. Pascal Auscher, Alan McIntosh, Emmanuel Russ, “Hardy Spaces of Differential Forms on Riemannian Manifolds”, J Geom Anal, 18:1 (2008), 192  crossref  mathscinet  zmath  isi
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    43. Gyrya P., Saloff-Coste L., “Neumann and Dirichlet Heat Kernels in Inner Uniform Domains”, Asterisque, 2011, no. 336, 1+  mathscinet  isi
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    46. Coulhon T., Kerkyacharian G., Petrushev P., “Heat Kernel Generated Frames in the Setting of Dirichlet Spaces”, J. Fourier Anal. Appl., 18:5 (2012), 995–1066  crossref  mathscinet  zmath  isi
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  • Математический сборник - 1991 Sbornik: Mathematics (from 1967)
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