Involutivity of truncated microsupports
Using a result of J.-M. Bony, we prove the weak involutivity of truncated microsupports. More precisely, given a sheaf on a real manifold and , if two functions vanish on , then so does their Poisson bracket.
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Masaki Kashiwara, Térésa Monteiro Fernandes, Pierre Schapira (2003)
Bulletin de la Société Mathématique de France
Using a result of J.-M. Bony, we prove the weak involutivity of truncated microsupports. More precisely, given a sheaf on a real manifold and , if two functions vanish on , then so does their Poisson bracket.
J. J. Duistermaat, I. M. Singer (1974/1975)
Séminaire Équations aux dérivées partielles (Polytechnique)
Shing-Tung Yau (1975)
Annales scientifiques de l'École Normale Supérieure
Isaac Chavel, Edgar A. Feldmann (1983)
Mathematische Zeitschrift
Marcello Lucia (2009)
Annales de l'I.H.P. Analyse non linéaire
Ruishi Kuwabara (1990)
Mathematische Zeitschrift
Carolyn S. Gordon, Ruth Gornet, Dorothee Schueth, David L. Webb, Edward N. Wilson (1998)
Annales de l'institut Fourier
We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds , more precisely, on , where is a torus of dimension and is a sphere of dimension . These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.
Jacques Gasqui, Hubert Goldschmidt (2007)
Annales de l’institut Fourier
We study the special Lagrangian Grassmannian , with , and its reduced space, the reduced Lagrangian Grassmannian . The latter is an irreducible symmetric space of rank and is the quotient of the Grassmannian under the action of a cyclic group of isometries of order . The main result of this paper asserts that the symmetric space possesses non-trivial infinitesimal isospectral deformations. Thus we obtain the first example of an irreducible symmetric space of arbitrary rank , which is...
Dorothee Schueth (1995)
Commentarii mathematici Helvetici
Isangulov, R.R. (2004)
Sibirskij Matematicheskij Zhurnal
Isangulov, R.R. (2006)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
Robert Brooks (1996/1997)
Séminaire de théorie spectrale et géométrie
Doyle, Peter G., Rossetti, Juan Pablo (2008)
The New York Journal of Mathematics [electronic only]
C. Gordon, D. Webb, S. Wolpert (1992)
Inventiones mathematicae
Peter Buser (1986)
Annales de l'institut Fourier
We construct new examples of compact Riemann surfaces which are non isometric but have the same spectrum of the Laplacian. Examples are given for genus and for all . In a second part we give examples of isospectral non isometric surfaces in which are realizable by paper models.
Laurent Charles, Álvaro Pelayo, San Vũ Ngoc (2013)
Annales scientifiques de l'École Normale Supérieure
We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians. This type of...
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