The Ricci iteration and its applications [PDF]
, 2007 In this Note we introduce and study dynamical systems related to the Ricci operator on the space of Kahler metrics as discretizations of certain geometric flows.
Rubinstein, Yanir A.
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On the bifurcation of solutions of the Yamabe problem in product manifolds with minimal boundary
Advances in Nonlinear Analysis, 2018 In this paper, we study the multiplicity of solutions of the Yamabe problem on product manifolds with minimal boundary via bifurcation theory.
Cárdenas Diaz Elkin Dario +1 more
doaj +1 more source
Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces [PDF]
, 2016 Recently Penskoi [J. Geom. Anal. 25 (2015), 2645-2666, arXiv:1308.1628] generalized the well known two-parametric family of Lawson tau-surfaces $\tau_{r,m}$ minimally immersed in spheres to a three-parametric family $T_{a,b,c}$ of tori and Klein bottles ...
Causley, Broderick
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Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds [PDF]
, 2009 We give upper bounds for the eigenvalues of the La-place-Beltrami operator of a compact $m$-dimensional submanifold $M$ of $\R^{m+p}$. Besides the dimension and the volume of the submanifold and the order of the eigenvalue, these bounds depend on either ...
Colbois, Bruno +2 more
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Local extremality of the Calabi-Croke sphere for the length of the shortest closed geodesic [PDF]
, 2009 Recently, F. Balacheff proved that the Calabi-Croke sphere made of two flat 1-unit-side equilateral triangles glued along their boundaries is a local extremum for the length of the shortest closed geodesic among the Riemannian spheres with conical ...
Sabourau, Stephane
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Extremal Eigenvalues of the Laplacian on Euclidean domains and closed surfaces [PDF]
, 2014 We investigate properties of the sequences of extremal values that could be achieved by the eigenvalues of the Laplacian on Euclidean domains of unit volume, under Dirichlet and Neumann boundary conditions, respectively.
Ahmad, Bruno Colbois, El Soufi
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Bifurcation of periodic solutions to the singular Yamabe problem on spheres [PDF]
, 2015 We obtain uncountably many periodic solutions to the singular Yamabe problem on a round sphere, that blow up along a great circle. These are (complete) constant scalar curvature metrics on the complement of $S^1$ inside $S^m$, $m\geq 5$, that are ...
Bettiol, Renato G. +2 more
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On the Critical Points of the E_k Functionals in Kahler Geometry
, 2006 We prove that a Kahler metric in the anticanonical class which is a critical point of the functional E_k and has nonnegative Ricci curvature, is necessarily Kahler-Einstein.
Tosatti, Valentino
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Generalized Lawson tori and Klein bottles [PDF]
, 2013 Using Takahashi theorem we propose an approach to extend known families of minimal tori in spheres. As an example, the well-known two-parametric family of Lawson tau-surfaces including tori and Klein bottles is extended to a three-parametric family of ...
Penskoi, Alexei V.
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Non-maximality of known extremal metrics on torus and Klein bottle
, 2013 El Soufi-Ilias' theorem establishes a connection between minimal submanifolds of spheres and extremal metrics for eigenvalues of the Laplace-Beltrami operator.
Karpukhin, Mikhail A.
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