Józef Dodziuk | Graduate Center of the City University of New York (original) (raw)

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Marc Frisch

Université Sorbonne Paris Nord / Sorbonne Paris Nord University

Frederic Barbaresco

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Papers by Józef Dodziuk

Research paper thumbnail of La trace du noyau de la chaleur des variétés hyperboliques de dimension 3

Séminaire de théorie spectrale et géométrie, 1996

L'accès aux archives de la revue « Séminaire de Théorie spectrale et géométrie » implique l'accor... more L'accès aux archives de la revue « Séminaire de Théorie spectrale et géométrie » implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Séminaire de théorie spectrale et géométrie GRENOBLE 1995-1996 (53-57) LA TRACE DU NOYAU DE LA CHALEUR DES VARIÉTÉS HYPERBOLIQUES DE DIMENSION 3 Jozef DODZIUK RÉSUMÉ .-D'après un théorème de W. Thurston, toute variété Mo hyperbolique, complète, non compacte, de volume fini et de dimension 3 est limite d'une suite des variétés AS* du même type avec moins de cusps. On va discuter le comportement de la trace de l'opérateur de la chaleur pendant la convergence M*-• Mo.

Research paper thumbnail of Elliptic operators on infinite graphs

We present some applications of ideas from partial differential equations and differential geomet... more We present some applications of ideas from partial differential equations and differential geometry to the study of difference equations on infinite graphs. All operators that we consider are examples of "elliptic operators" as defined by Y. Colin de Verdiere. For such operators, we discuss analogs of inequalities of Cheeger and Harnack and of the maximum principle (in both elliptic and

Research paper thumbnail of Maximum principle for parabolic inequalities and the heat flow on open mani-folds

Research paper thumbnail of Finite-difference approach to the Hodge theory of harmonic forms

Research paper thumbnail of Nonexistence of universal upper bounds for the first positive eigenvalue of the Laplace-Beltrami operator

Contemporary Mathematics, 1994

Research paper thumbnail of Vanishing theorems for square-integrable harmonic forms

Proceedings Mathematical Sciences, 1981

There are two ways of proving vanishing theorems for cohomology of compact Riem&rmian manifolds. ... more There are two ways of proving vanishing theorems for cohomology of compact Riem&rmian manifolds. One is based on Bochner's lemma, a variant of maximum principle, the other is an application of Weitzenb6ck identity and integration by parts. Both are discussed in great detail in . In this paper we show that the latter method yields vanishing theorems for L2-1~rmonic forms on complete manifolds. The extra ingredient required in the proof is due to Andreotti arid Vesentini [1]; (see also , theorem 26).

Research paper thumbnail of Combinatorial and continuous Hodge theories

Bulletin of the American Mathematical Society, 1974

Research paper thumbnail of Appendix Laplacian on Forms

Pure and Applied Mathematics, 1984

Research paper thumbnail of ELLIPTIC OPERATORS ON INFINITE GRAPHS

Papers in Honor of Krzysztof P Wojciechowski, 2006

We present some applications of ideas from partial differential equations and differential geomet... more We present some applications of ideas from partial differential equations and differential geometry to the study of difference equations on infinite graphs. All operators that we consider are examples of "elliptic operators" as defined by Y. Colin de Verdiere . For such operators, we discuss analogs of inequalities of Cheeger and Harnack and of the maximum principle (in both elliptic and parabolic versions), and apply them to study spectral theory, the ground state and the heat semigroup associated to these operators.

Research paper thumbnail of ELLIPTIC OPERATORS ON INFINITE GRAPHS This work is supported in part by a PSC-CUNY Research Grant

Research paper thumbnail of Review: Peter B. Gilkey, Invariance theory, the heat equation, and the Atiyah-Singer index theorem

Bulletin of The American Mathematical Society - BULL AMER MATH SOC, 1986

Research paper thumbnail of Difference Equations, Isoperimetric Inequality and Transience of Certain Random Walks

Transactions of the American Mathematical Society, 1984

... Our results are motivated by [Do], where transience of the Brownian motion on certain manifol... more ... Our results are motivated by [Do], where transience of the Brownian motion on certain manifolds was proved. ... <p{[x,y[) = -<p{[y,x]), where [x,y] denotes an oriented (directed) edge beginning at x and ending at y. For every edge of K we fix, once and for all, a direction. ...

Research paper thumbnail of De Rham-Hodge theory for L2-cohomology of infinite coverings

Research paper thumbnail of A Remark on Whitney's Proof of de Rham's Theorem

Proceedings of the American Mathematical Society, 1976

Research paper thumbnail of L 2 Harmonic Forms on Rotationally Symmetric Riemannian Manifolds

Proceedings of the American Mathematical Society, 1979

Research paper thumbnail of Eigenvalues of the Laplacian on forms

Proceedings of the American Mathematical Society, 1982

Research paper thumbnail of Sobolev spaces of differential forms and de Rham-Hodge isomorphism

Research paper thumbnail of Maximum principle for parabolic inequalities and the heat flow on open manifolds

Research paper thumbnail of Eigenvalues of the Laplacian and the Heat Equation

The American Mathematical Monthly, 1981

Research paper thumbnail of Finite-Difference Approach to the Hodge Theory of Harmonic Forms

American Journal of Mathematics, 1976

Research paper thumbnail of La trace du noyau de la chaleur des variétés hyperboliques de dimension 3

Séminaire de théorie spectrale et géométrie, 1996

L'accès aux archives de la revue « Séminaire de Théorie spectrale et géométrie » implique l'accor... more L'accès aux archives de la revue « Séminaire de Théorie spectrale et géométrie » implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Séminaire de théorie spectrale et géométrie GRENOBLE 1995-1996 (53-57) LA TRACE DU NOYAU DE LA CHALEUR DES VARIÉTÉS HYPERBOLIQUES DE DIMENSION 3 Jozef DODZIUK RÉSUMÉ .-D'après un théorème de W. Thurston, toute variété Mo hyperbolique, complète, non compacte, de volume fini et de dimension 3 est limite d'une suite des variétés AS* du même type avec moins de cusps. On va discuter le comportement de la trace de l'opérateur de la chaleur pendant la convergence M*-• Mo.

Research paper thumbnail of Elliptic operators on infinite graphs

We present some applications of ideas from partial differential equations and differential geomet... more We present some applications of ideas from partial differential equations and differential geometry to the study of difference equations on infinite graphs. All operators that we consider are examples of "elliptic operators" as defined by Y. Colin de Verdiere. For such operators, we discuss analogs of inequalities of Cheeger and Harnack and of the maximum principle (in both elliptic and

Research paper thumbnail of Maximum principle for parabolic inequalities and the heat flow on open mani-folds

Research paper thumbnail of Finite-difference approach to the Hodge theory of harmonic forms

Research paper thumbnail of Nonexistence of universal upper bounds for the first positive eigenvalue of the Laplace-Beltrami operator

Contemporary Mathematics, 1994

Research paper thumbnail of Vanishing theorems for square-integrable harmonic forms

Proceedings Mathematical Sciences, 1981

There are two ways of proving vanishing theorems for cohomology of compact Riem&rmian manifolds. ... more There are two ways of proving vanishing theorems for cohomology of compact Riem&rmian manifolds. One is based on Bochner's lemma, a variant of maximum principle, the other is an application of Weitzenb6ck identity and integration by parts. Both are discussed in great detail in . In this paper we show that the latter method yields vanishing theorems for L2-1~rmonic forms on complete manifolds. The extra ingredient required in the proof is due to Andreotti arid Vesentini [1]; (see also , theorem 26).

Research paper thumbnail of Combinatorial and continuous Hodge theories

Bulletin of the American Mathematical Society, 1974

Research paper thumbnail of Appendix Laplacian on Forms

Pure and Applied Mathematics, 1984

Research paper thumbnail of ELLIPTIC OPERATORS ON INFINITE GRAPHS

Papers in Honor of Krzysztof P Wojciechowski, 2006

We present some applications of ideas from partial differential equations and differential geomet... more We present some applications of ideas from partial differential equations and differential geometry to the study of difference equations on infinite graphs. All operators that we consider are examples of "elliptic operators" as defined by Y. Colin de Verdiere . For such operators, we discuss analogs of inequalities of Cheeger and Harnack and of the maximum principle (in both elliptic and parabolic versions), and apply them to study spectral theory, the ground state and the heat semigroup associated to these operators.

Research paper thumbnail of ELLIPTIC OPERATORS ON INFINITE GRAPHS This work is supported in part by a PSC-CUNY Research Grant

Research paper thumbnail of Review: Peter B. Gilkey, Invariance theory, the heat equation, and the Atiyah-Singer index theorem

Bulletin of The American Mathematical Society - BULL AMER MATH SOC, 1986

Research paper thumbnail of Difference Equations, Isoperimetric Inequality and Transience of Certain Random Walks

Transactions of the American Mathematical Society, 1984

... Our results are motivated by [Do], where transience of the Brownian motion on certain manifol... more ... Our results are motivated by [Do], where transience of the Brownian motion on certain manifolds was proved. ... <p{[x,y[) = -<p{[y,x]), where [x,y] denotes an oriented (directed) edge beginning at x and ending at y. For every edge of K we fix, once and for all, a direction. ...

Research paper thumbnail of De Rham-Hodge theory for L2-cohomology of infinite coverings

Research paper thumbnail of A Remark on Whitney's Proof of de Rham's Theorem

Proceedings of the American Mathematical Society, 1976

Research paper thumbnail of L 2 Harmonic Forms on Rotationally Symmetric Riemannian Manifolds

Proceedings of the American Mathematical Society, 1979

Research paper thumbnail of Eigenvalues of the Laplacian on forms

Proceedings of the American Mathematical Society, 1982

Research paper thumbnail of Sobolev spaces of differential forms and de Rham-Hodge isomorphism

Research paper thumbnail of Maximum principle for parabolic inequalities and the heat flow on open manifolds

Research paper thumbnail of Eigenvalues of the Laplacian and the Heat Equation

The American Mathematical Monthly, 1981

Research paper thumbnail of Finite-Difference Approach to the Hodge Theory of Harmonic Forms

American Journal of Mathematics, 1976

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