Results 21 to 30 of about 79,734 (334)
Uniform stability of twisted constant scalar curvature K\"ahler metrics [PDF]
, 2014 We introduce a norm on the space of test configurations, which we call the minimum norm. We conjecture that uniform K-stability with respect to this norm is equivalent to the existence of a constant scalar curvature K\"ahler metric.
R. Dervan
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Liouville theorem on Ricci shrinkers with constant scalar curvature and its application [PDF]
Journal für die Reine und Angewandte Mathematik, 2022 In this paper we consider harmonic functions on gradient shrinking Ricci solitons with constant scalar curvature. A Liouville theorem is proved without using gradient estimate: any bounded harmonic function is constant on gradient shrinking Ricci ...
Weixiong Mai, Jianyu Ou
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K-stability of constant scalar curvature Kähler manifolds
Advances in Mathematics, 2009 We show that a polarised manifold with a constant scalar curvature Kähler metric and discrete automorphisms is K-stable. This refines the K-semistability proved by S. K. Donaldson.
Stoppa, J., Stoppa, Jacopo
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Conformal deformations of conic metrics to constant scalar curvature [PDF]
, 2021 We consider conformal deformations within a class of incomplete Riemannian metrics which generalize conic orbifold singularities by allowing both warping and any compact manifold (not just quotients of the sphere) to be the ``link'' of the singular set ...
Thalia D. Jeffres, J. Rowlett
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SCALAR CURVATURE OF HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A SPHERE [PDF]
Glasgow Mathematical Journal, 2009 AbstractLet M be an n-dimensional closed hypersurface with constant mean curvature H satisfying |H| ≤ ϵ(n) in a unit sphere Sn+1, n ≤ 7, and S the square of the length of the second fundamental form of M. There exists a constant δ(n, H) > 0, which depends only on n and H, such that if S0 ≤ S ≤ S0 + δ(n, H), then S ≡ S0 and M is isometric to a ...
Cheng, Qing-Ming +2 more
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On hypersurfaces of Lorentzian standard 4-space forms satisfying a biconservativity condition [PDF]
Journal of Mahani Mathematical Research, 2023 In this manuscript, we consider an extended version of biconservativity condition (namely, ${\textrm C}$-biconservativity) on the Riemannian hypersurfaces of Lorentzian standard 4-space forms.
Firooz Pashaie
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Metrics of constant negative scalar-Weyl curvature [PDF]
, 2023 Extending Aubin's construction of metrics with constant negative scalar curvature, we prove that every n-dimensional closed manifold admits a Riemannian metric with constant negative scalarWeyl curvature, that is R + t|W|, t is an element of R.
Catino, Giovanni
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Lectures on Stability and Constant Scalar Curvature [PDF]
Current Developments in Mathematics, 2007 An introduction is provided to some current research trends in stability in geometric invariant theory and the problem of Kaehler metrics of constant scalar curvature. Besides classical notions such as Chow-Mumford stability, the emphasis is on several new stability conditions, such as K-stability, Donaldson's infinite-dimensional GIT, and conditions ...
Phong, D.H., Sturm, Jacob
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Stable Hypersurfaces with Constant Scalar Curvature [PDF]
Mathematische Zeitschrift, 1993 It is well known that hypersurfaces with constant mean curvature in Riemannian spaces are solutions to the variational problem of minimizing area for volume-preserving variations. Less known is the fact that hypersurfaces with constant scalar curvature in Riemannian spaces of constant sectional curvature are also solutions to a variational problem ...
Carmo, M. do, Alencar, H., Colares, A.G.
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Metrics of Eguchi–Hanson types with the negative constant scalar curvature [PDF]
, 2020 We construct two types of Eguchi-Hanson metrics with the negative constant scalar curvature. The type I metrics are Kahler. The type II metrics are ALH whose total energy can be negative.
Junwen Chen, Xiao Zhang
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