Isoperimetric problems on the sphere and on surfaces with density.
Isoperimetric profile and uniqueness for Neumann problems
Isoperimetric regions in the plane with density .
Isoperimetric Symmetry Breaking: a Counterexample to a Generalized Form of the Log-Convex Density Conjecture
We give an example of a smooth surface of revolution for which all circles about the origin are strictly stable for fixed area but small isoperimetric regions are nearly round discs away from the origin.
Isopérimétrie pour les groupes et les variétés.
Dans cet article, nous proposons une approche très directe de différents inégalités isopérimétriques.
Isoperimetrische Ungleichungen für geschlossene Kurven
Isoperimetrische Ungleichungen für räumliche Kurven und Polygone
Isoptics of a closed strictly convex curve. - II
Isoptics of pairs of nested closed strictly convex curves and Crofton-type formulas.
Isospectral Connections on Line Bundles.
Isospectral deformations of closed riemannian manifolds with different scalar curvature
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.
Isospectral deformations of the Lagrangian Grassmannians
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...
Isospectral deformations on Riemannian manifolds which are diffeomorphic to compact Heisenberg manifolds.
Isospectral hyperbolic surfaces have matching geodesics.
Isospectral, non-isometric Riemannian manifolds
The author gives a survey of the history of isospectral manifolds that are non-isometric discussing the work of Milnor, Vignéras, Sunada, and de Turck and Gordon. She describes the construction of continuous isospectral deformations as introduced by Gordon, Wilson, De Turck et al. She also discusses the construction of isospectral plane domains due to Gordon, Webb, and Wolpert. Some new examples of isospectral non-isometric manifolds are given.
Isospectral Riemann surfaces
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.
Isospectrality for quantum toric integrable systems
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...
Isothermic surfaces and Hopf cylinders.
Isothermic surfaces as solutions of Calapso PDE.
Isotopy of sympletic balls, Gromov' s radius and the structure of ruled symplectic 4-manifolds.