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Differential invariants of generic hyperbolic Monge-Ampère equations

Michal Marvan, Alexandre Vinogradov, Valery Yumaguzhin (2007)

Open Mathematics

In this paper basic differential invariants of generic hyperbolic Monge-Ampère equations with respect to contact transformations are constructed and the equivalence problem for these equations is solved.

Dirac operators on hypersurfaces

Jarolím Bureš (1993)

Commentationes Mathematicae Universitatis Carolinae

In this paper some relation among the Dirac operator on a Riemannian spin-manifold N , its projection on some embedded hypersurface M and the Dirac operator on M with respect to the induced (called standard) spin structure are given.

Discrete version of Dungey’s proof for the gradient heat kernel estimate on coverings

Satoshi Ishiwata (2007)

Annales mathématiques Blaise Pascal

We obtain another proof of a Gaussian upper estimate for a gradient of the heat kernel on cofinite covering graphs whose covering transformation group has a polynomial volume growth. It is proved by using the temporal regularity of the discrete heat kernel obtained by Blunck [2] and Christ [3] along with the arguments of Dungey [7] on covering manifolds.

Discreteness of the spectrum for some differential operators with unbounded coefficients in R n

Giorgio Metafune, Diego Pallara (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We give sufficient conditions for the discreteness of the spectrum of differential operators of the form A u = - u + F , u in L μ 2 R n where d μ x = e - F x d x and for Schrödinger operators in L 2 R n . Our conditions are also necessary in the case of polynomial coefficients.

Discrétisation de zeta-déterminants d’opérateurs de Schrödinger sur le tore

Laurent Chaumard (2006)

Bulletin de la Société Mathématique de France

Nous donnons ici deux résultats sur le déterminant ζ -régularisé det ζ A d’un opérateur de Schrödinger A = Δ g + V sur une variété compacte . Nous construisons, pour = S 1 × S 1 , une suite ( G n , ρ n , Δ n ) G n est un graphe fini qui se plonge dans via ρ n de telle manière que ρ n ( G n ) soit une triangulation de et où  Δ n est un laplacien discret sur G n tel que pour tout potentiel V sur , la suite de réels det ( Δ n + V ) converge après renormalisation vers det ζ ( Δ g + V ) . Enfin, nous donnons sur toute variété riemannienne compacte ( , g ) de dimension inférieure ou égale à 3 ...

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