Grigor’yan, Alexander; Nadirashvili, Nikolai; Sire, Yannick A lower bound for the number of negative eigenvalues of Schrödinger operators. (English) Zbl 1356.53044 J. Differ. Geom. 102, No. 3, 395-408 (2016). Reviewer: Lizhen Ji (Ann Arbor) MSC: 53C21 58J50 35P15 PDFBibTeX XMLCite \textit{A. Grigor'yan} et al., J. Differ. Geom. 102, No. 3, 395--408 (2016; Zbl 1356.53044) Full Text: DOI arXiv Euclid
Grigor’yan, Alexander Heat kernel and analysis on manifolds. (English) Zbl 1206.58008 AMS/IP Studies in Advanced Mathematics 47. Providence, RI: American Mathematical Society (AMS); Somerville, MA: International Press (ISBN 978-0-8218-4935-4/hbk). xvii, 482 p. (2009). Reviewer: Ilka Agricola (Marburg) MSC: 58J35 53C20 58-02 31B05 35K05 35P15 47D07 PDFBibTeX XMLCite \textit{A. Grigor'yan}, Heat kernel and analysis on manifolds. Providence, RI: American Mathematical Society (AMS); Somerville, MA: International Press (2009; Zbl 1206.58008) Backlinks: MO MO
Grigor’yan, Alexander (ed.); Yau, Shing Tung (ed.) Surveys in differential geometry. Vol. IX: Eigenvalues of Laplacians and other geometric operators. (English) Zbl 1050.53002 Surveys in Differential Geometry 9. Somerville, MA: International Press (ISBN 1-57146-115-9/hbk). iii, 467 p. (2004). MSC: 53-06 58-06 00B25 PDFBibTeX XMLCite \textit{A. Grigor'yan} (ed.) and \textit{S. T. Yau} (ed.), Surveys in differential geometry. Vol. IX: Eigenvalues of Laplacians and other geometric operators. Somerville, MA: International Press (2004; Zbl 1050.53002) Full Text: Link
Coulhon, Thierry; Grigor’yan, Alexander; Levin, Daniel On isoperimetric profiles of product spaces. (English) Zbl 1085.53027 Commun. Anal. Geom. 11, No. 1, 85-120 (2003). Reviewer: Marian Hotloś (Wrocław) MSC: 53C20 46E35 26D10 PDFBibTeX XMLCite \textit{T. Coulhon} et al., Commun. Anal. Geom. 11, No. 1, 85--120 (2003; Zbl 1085.53027) Full Text: DOI
Grigor’yan, Alexander Isoperimetric inequalities and capacities on Riemannian manifolds. (English) Zbl 0947.58034 Rossmann, Jürgen (ed.) et al., The Maz’ya anniversary collection. Vol. 1: On Maz’ya’s work in functional analysis, partial differential equations and applications. Based on talks given at the conference, Rostock, Germany, August 31-September 4, 1998. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 109, 139-153 (1999). Reviewer: Yu.E.Gliklikh (Voronezh) MSC: 58J65 53C20 58-03 01A65 53-03 PDFBibTeX XMLCite \textit{A. Grigor'yan}, in: The Maz'ya anniversary collection. Vol. 1: On Maz'ya's work in functional analysis, partial differential equations and applications. Based on talks given at the conference, Rostock, Germany, August 31--September 4, 1998. Basel: Birkhäuser. 139--153 (1999; Zbl 0947.58034)
Grigor’yan, Alexander Gaussian upper bounds for the heat kernel on arbitrary Riemannian manifolds. (English) Zbl 0865.58042 J. Differ. Geom. 45, No. 1, 33-52 (1997). Reviewer: A.Grigor’yan (London) MSC: 58J35 53C20 PDFBibTeX XMLCite \textit{A. Grigor'yan}, J. Differ. Geom. 45, No. 1, 33--52 (1997; Zbl 0865.58042) Full Text: DOI
Chung, F. R. K.; Grigor’yan, A.; Yau, Shing-Tung Upper bounds for eigenvalues of the discrete and continuous Laplace operators. (English) Zbl 0844.53029 Adv. Math. 117, No. 2, 165-178 (1996). Reviewer: P.Gilkey (Eugene) MSC: 53C20 58J50 PDFBibTeX XMLCite \textit{F. R. K. Chung} et al., Adv. Math. 117, No. 2, 165--178 (1996; Zbl 0844.53029) Full Text: DOI Link
Grigor’yan, A. A. Dimension of spaces of harmonic functions. (English. Russian original) Zbl 0721.31003 Math. Notes 48, No. 5, 1114-1118 (1990); translation from Mat. Zametki 48, No. 5, 55-61 (1990). Reviewer: W.Okrasiński (Wrocław) MSC: 31C05 53C20 PDFBibTeX XMLCite \textit{A. A. Grigor'yan}, Math. Notes 48, No. 5, 1114--1118 (1990; Zbl 0721.31003); translation from Mat. Zametki 48, No. 5, 55--61 (1990) Full Text: DOI
Grigor’yan, A. A. A criterion for the existence on a Riemannian manifold of a nontrivial bounded harmonic function with finite Dirichlet integral. (English. Russian original) Zbl 0644.31007 Sov. Math., Dokl. 35, 339-341 (1987); translation from Dokl. Akad. Nauk SSSR 293, 529-531 (1987). Reviewer: M.Dont MSC: 31C12 53C20 PDFBibTeX XMLCite \textit{A. A. Grigor'yan}, Sov. Math., Dokl. 35, 339--341 (1987; Zbl 0644.31007); translation from Dokl. Akad. Nauk SSSR 293, 529--531 (1987)
Grigor’yan, A. A. Isoperimetric inequalities for Riemannian products. (English. Russian original) Zbl 0599.53035 Math. Notes 38, 849-854 (1985); translation from Mat. Zametki 38, No. 4, 617-626 (1985). Reviewer: W.Mozgawa MSC: 53C20 PDFBibTeX XMLCite \textit{A. A. Grigor'yan}, Math. Notes 38, 849--854 (1985; Zbl 0599.53035); translation from Mat. Zametki 38, No. 4, 617--626 (1985) Full Text: DOI
Grigor’yan, A. A. On the existence of a Green’s function on a manifold. (English. Russian original) Zbl 0542.35025 Russ. Math. Surv. 38, No. 1, 190-191 (1983); translation from Usp. Mat. Nauk 38, No. 1(229), 161-162 (1983). Reviewer: J.Appell MSC: 35J05 35C15 53C20 31C12 PDFBibTeX XMLCite \textit{A. A. Grigor'yan}, Russ. Math. Surv. 38, No. 1, 190--191 (1983; Zbl 0542.35025); translation from Usp. Mat. Nauk 38, No. 1(229), 161--162 (1983) Full Text: DOI
Grigor’yan, A. A. On a theorem of Liouville type on a Riemannian manifold. (Russian. English summary) Zbl 0577.53032 Tr. Tbilis. Univ. 232/233, Mat. Mekh. Astron. 13/14, 49-77 (1982). Reviewer: W.Mozgawa MSC: 53C20 PDFBibTeX XML
Grigor’yan, A. A. A Liouville theorem on a manifold. (English) Zbl 0552.53018 Russ. Math. Surv. 37, No. 3, 209-210 (1982). MSC: 53C20 58J60 35J05 PDFBibTeX XMLCite \textit{A. A. Grigor'yan}, Russ. Math. Surv. 37, No. 3, 209--210 (1982; Zbl 0552.53018) Full Text: DOI
Grigor’yan, A. A. On a certain Liouville theorem on a manifold. (Russian) Zbl 0509.53035 Usp. Mat. Nauk 37, No. 3(225), 181-182 (1982). MSC: 53C20 35J05 58J60 PDFBibTeX XMLCite \textit{A. A. Grigor'yan}, Usp. Mat. Nauk 37, No. 3(225), 181--182 (1982; Zbl 0509.53035)