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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 $g = 5$ and for all $g \geq 7$ . In a second part we give examples of isospectral non isometric surfaces in $R^{3}$ which are realizable by paper models.

Isospectrality for quantum toric integrable systems

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...

Isotopie de formes fermées en dimension trois.

Francois Laudenbach, Samuel Blank (1979)

Inventiones mathematicae

Isotropic characteristic classes

Jean-Marie Morvan, Louis Niglio (1994)

Compositio Mathematica

Isotropy representation of flag manifolds

Alekseevsky, D. V. (1998)

Proceedings of the 17th Winter School "Geometry and Physics"

A flag manifold of a compact semisimple Lie group $G$ is defined as a quotient $M = G / K$ where $K$ is the centralizer of a one-parameter subgroup $exp (t x)$ of $G$ . Then $M$ can be identified with the adjoint orbit of $x$ in the Lie algebra $𝒢$ of $G$ . Two flag manifolds $M = G / K$ and $M^{'} = G / K^{'}$ are equivalent if there exists an automorphism $φ : G \to G$ such that $φ (K) = K^{'}$ (equivalent manifolds need not be $G$ -diffeomorphic since $φ$ is not assumed to be inner). In this article, explicit formulas for decompositions of the isotropy representation for all flag manifolds...

Iterated Integrals and Homotopy Periods

Bohumil Cenkl (1976)

Publications du Département de mathématiques (Lyon)

Iterates approaching hyperbolic manifolds of fixed points.

Bernd Aulbach (1984)

Journal für die reine und angewandte Mathematik

Iterative processes and open mapping theorems

Stephen Dancs (1989)

Czechoslovak Mathematical Journal

Iterative schemes to solve nonconvex variational problems.

Bounkhel, Messaoud, Tadj, Lotfi, Hamdi, Abdelouahed (2003)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Ito equation as a geodesic flow on $\hat{{Diff}^{s} (S^{1}) ⨀ C^{\infty} (S^{1})}$

Partha Guha (2000)

Archivum Mathematicum

The Ito equation is shown to be a geodesic flow of $L^{2}$ metric on the semidirect product space $\hat{{𝐷𝑖𝑓𝑓}^{s} (S^{1}) ⨀ C^{\infty} (S^{1})}$ , where ${𝐷𝑖𝑓𝑓}^{s} (S^{1})$ is the group of orientation preserving Sobolev $H^{s}$ diffeomorphisms of the circle. We also study a geodesic flow of a $H^{1}$ metric.

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