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Metric inequalities with scalar curvature

WebDefinition. Given a Riemannian metric g, the scalar curvature S (commonly also R, or Sc) is defined as the trace of the Ricci curvature tensor with respect to the metric: = ⁡. The scalar curvature cannot be computed directly from the Ricci curvature since the latter is a (0,2)-tensor field; the metric must be used to raise an index to obtain a (1,1)-tensor field … Web19 aug. 2015 · A well-known question in differential geometry is to control the constant in isoperimetric inequality by intrinsic curvature conditions. In dimension 2, the constant can be controlled by the integral of the positive part of the Gaussian curvature.

(PDF) Scalar curvature rigidity of certain symmetric spaces

Web23 dec. 2024 · [2012.12478] Waist inequality for 3-manifolds with positive scalar curvature We construct singular foliations of compact three-manifolds $(M^3,h)$ with scalar curvature $R_h\geq Λ_0>0$ by surfaces of controlled area, diameter This extends Urysohn and waist... Global Survey In just 3 minutes help us understand how you see … WebBased on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin manifolds of infinite K-area. We also characterize the extremal case. Next we show a general deformation principle for boundary conditions of metrics with lower scalar curvature bounds. This implies that … greg milligan country singer https://inadnubem.com

Metric Inequalities with Scalar Curvature Semantic Scholar

WebWe establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below. WebA Riemannian manifold endowed with k>2 orthogonal complementary distributions (called here an almost multi-product structure) appears in such topics as multiply twisted or warped products and the webs or nets composed of orthogonal foliations. In this article, we define the mixed scalar curvature of an almost multi-product structure endowed with a linear … WebPositive scalar curvature and exotic aspherical manifolds - Jialong DENG 邓嘉龙, YMSC Scalar curvature is interesting not only in analysis, geometry and topology but also in physics. For example, the positive mass theorem, which was proved by Schoen and Yau in 1979, is equivalent to the result that the three-dimension torus carries no Riemannian … greg minor mechanics

Kummer-type constructions of almost Ricci-flat 5-manifolds

Category:Metric Inequalities with Scalar Curvature. - ar5iv.labs.arxiv.org

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Metric inequalities with scalar curvature

[PDF] On closed surfaces with nonnegative curvature in the …

WebIn differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold.It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs locally from that of ordinary Euclidean space or … WebWe establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below. In so far as geometry is …

Metric inequalities with scalar curvature

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WebThe Penrose inequality in general relativity and volume comparison theorems involving scalar curvature, Ph.D. Thesis, Stanford University, 1997, arXiv:0902.3241 . Brendle S., Rigidity phenomena involving scalar curvature, in Surveys in Differential Geometry, Surv. Differ. Geom., Vol. 17, Int. Press, Boston, MA, 2012, 179-202, arXiv:1008.3097 . WebABSTRACT: Based on Donaldson’s method, we prove that, for an integral Kähler class, when there is a Kähler metric of constant scalar curvature, then it minimizes the K-energy. We do not assume that the automorphism gro…

Web11 jun. 2024 · We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below. In so far as geometry is concerned these inequalities appear as generalisations of the classical bounds on … WebIt is well known that if g is a smooth metric on M with unit volume and with scalar curvature 𝒮 ( g) ≥ σ ( M), then g is Einstein. We show, in all dimensions, the same is true for metrics with edge singularities with cone angles ≤ 2 π along codimension-2 submanifolds.

WebWe establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical … Web1 jun. 2024 · Abstract We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below. In so far as geometry is...

WebMetric Inequalities with Scalar Curvature. Misha Gromov Abstract We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the …

Web1 jun. 2004 · This paper considers the prescribed zero scalar curvature and mean curvature problem on the n -dimensional Euclidean ball for n ⩾3. We consider the limits … greg mist flowerWebvature, i.e. integral of scalar curvature over the whole manifold. We shall see in the below that this equation has good behaviour for manifolds with posi-tive curvature. By studying its convergence behaviour, Hamilton obtained the following result: Theorem 1.1. Let X be a compact 3-manifold which admits a Riemannian metric with positive Ricci ... greg mitchell express scriptsWebIn this article we obtain a priori estimates for solutions to the prescribed scalar curvature equation on 2- and 3-spheres under a nondegeneracy ... Metric Inequalities with Scalar Curvature. 11 June ... Schoen, R.: Conformal metrics with prescribed scalar curvature. Invent. Math.86, 243–254 (1986) Google Scholar Gursky, M ... greg mitchell woodbury tnWeb4 apr. 2024 · In this paper, we study the existence of conformal metrics with constant holomorphic d-scalar curvature and the prescribed holomorphic d-scalar curvature problem on closed, connected almost Hermitian manifolds of dimension n ⩾ 6. In addition, we obtain an application and a variational formula for the associated conformal invariant. greg mitchell attorney oklahoma cityWeb12 okt. 2024 · We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces with positive sectional curvature. greg mitchell motors omaghWebWe establish several inequalities for manifolds with positive scalar cur-vature and, more generally, for the scalar curvature bounded from below. In so far as geometry is … greg mitchell motors - strabaneWebWe establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below. In so far as geometry is … greg mitchell substack