Results 11 to 20 of about 7,459 (148)
Kodaira Dimension and the Yamabe Problem [PDF]
Communications in Analysis and Geometry, 1997 The Yamabe invariant Y(M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unit-volume constant-scalar curvature Riemannian metrics g on M.
LeBrun, Claude
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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
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Discrete Yamabe Problem for Polyhedral Surfaces. [PDF]
Discrete Comput Geom, 2023 AbstractWe study a new discretization of the Gaussian curvature for polyhedral surfaces. This discrete Gaussian curvature is defined on each conical singularity of a polyhedral surface as the quotient of the angle defect and the area of the Voronoi cell corresponding to the singularity.
Dal Poz Kouřimská H.
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The Yamabe problem on Dirichlet spaces [PDF]
, 2013 We continue our previous work studying critical exponent semilinear elliptic (and subelliptic) problems which generalize the classical Yamabe problem. In [3] the focus was on metric-measure spaces with an `almost smooth' structure, with stratified spaces
Gilles Carron +3 more
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About the Lorentzian Yamabe problem [PDF]
Geometriae Dedicata, 2014 We investigate the solutions to the Yamabe problem on globally hyperbolic spacetimes. On standard static spacetimes, we prove the existence of global solutions and show with the help of examples that uniqueness does not hold in general.
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On a fully nonlinear Yamabe problem [PDF]
Annales Scientifiques de l’École Normale Supérieure, 2006 We solve the $ _2$-Yamabe problem for a non locally conformally flat manifold of dimension $n>8$.
Ge, Yuxin, Wang, Guofang
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Equivariant Yamabe problem and Hebey–Vaugon conjecture
Journal of Functional Analysis, 2010 In their study of the Yamabe problem in the presence of isometry group, Hebey and Vaugon announced a conjecture. This conjecture generalizes Aubin's conjecture, which has already been proven and is sufficient to solve the Yamabe problem. In this paper, we generalize Aubin's theorem and we prove the Hebey--Vaugon conjecture in some new cases.
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On the Chern–Yamabe problem [PDF]
Mathematical Research Letters, 2017 We initiate the study of an analogue of the Yamabe problem for complex manifolds. More precisely, fixed a conformal Hermitian structure on a compact complex manifold, we are concerned in the existence of metrics with constant Chern scalar curvature.
ANGELLA, DANIELE +2 more
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Bulletin of the American Mathematical Society, 1987 This is a basically self-contained account of the solution to the Yamabe problem, covering the steps due to Yamabe, Trudinger, Aubin and Schoen and including Witten's proof of the positive mass theorem. The presentation contains various improvements over arguments existing in the literature.
Lee, John M., Parker, Thomas H.
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A note on Chern-Yamabe problem [PDF]
Differential Geometry and its Applications, 2020 We propose a flow to study the Chern-Yamabe problem and discuss the long time existence of the flow. In the balanced case we show that the Chern-Yamabe problem is the Euler-Lagrange equation of some functional. The monotonicity of the functional along the flow is derived. We also show that the functional is not bounded from below.
Calamai, Simone, Zou, Fangyu
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