Metric inequalities with scalar curvature

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August undefined, 2024

Web26 aug. 2024 · We also derive explicit quantitative distance estimates in case the scalar curvature is uniformly positive in some region of the chosen end $\mathcal{E}$. Here we … 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 …

arXiv:1710.04655v3 [math.DG] 29 Oct 2024

WebThis inequality agrees with the obvious one in the 2-sphere (where the conventionally deﬁned scalar curvature equals twice the sectional curvature) where the widths of the … 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 … deep baking pans with handles

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Webvature, 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 ... WebThere are metrics with zero scalar curvature but nonvanishing Ricci curvature. For example, there is a complete Riemannian metric on the tautological line bundle over real … WebMetric Inequalities with Scalar Curvature. Misha Gromov We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the … federal tax rate for 250000 income

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Web14 dec. 2024 · Area and Gauss-Bonnet inequalities with scalar curvature. Misha Gromov, Jintian Zhu. Let be an -dimensional Riemannian manifold with "large positive" scalar curvature. In this paper, we prove in a variety of cases that if "spreads" in directions {\it "distance-wise"}, then it {\it can't} much "spread" in the remaining 2-directions {\it "area ... 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 … federal tax rate for 50000 annual salaryWeb12 okt. 2024 · Abstract: We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the … deep baking pan with rack

"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. " - Metric inequalities with scalar curvature

Metric inequalities with scalar curvature

Three-manifolds with positive Ricci 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 … WebLeth be a complete metric of Gaussian curvature K0 on a punctured Riemann surface of genusg ≥ 1 (or the sphere with at least three punctures). Given a smooth negative functionK withK =K 0 in neighbourhoods of the punctures we prove that there exists a metric conformal toh which attains this function as its Gaussian curvature for the punctured …

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Web31 aug. 2024 · There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly nonlinear scalar field, which allow the appearance of singularities of a new type (“spherical singularities”) … 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 …

Web1 okt. 2024 · In this paper, we study the interplay of geometry and positive scalar curvature on a complete, non-compact manifold with non-negative Ricci curvature. On three-dimensional manifold, ... , Metric inequalities with scalar curvature, Geom. Funct. Anal. 28 (2024), no. 3, 645–726. 10.1007/s00039-018-0453-z Search in Google Scholar 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 …

WebWe 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 … Web29 okt. 2024 · In the second part, we show that if M has positive scalar curvature, then the existence of non-trivial harmonic p-forms imposes a certain integral inequality …

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 …

Web12 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. federal tax rate filing singleWebA Riemannian manifold endowed with k>2 orthogonal complementary distributions (called here an almost multi-product structure) appears in such topics as multiply twisted or … federal tax rate for 60000 incomeWeb11 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 … deep barking cough adultWeb1 apr. 1995 · This is a short selected survey of results on scalar curvature rigidity of certain symmetric spaces, in particular, for the Euclidean, hyperbolic and spherical metrics. The proofs, all of which ... federal tax rate for 120 000 incomeWebABSTRACT: 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… federal tax rate for 94000Web4 apr. 2024 · Abstract. 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 … deep base fitted sheetWeb11 apr. 2024 · On one hand, it was argued that the Einstein–Hilbert action must be replaced by a more general setting, with particular reference to the simplest one of a metric f(R) gravity [5, 6]; on the other hand, it was suggested that a quantum dynamics of the gravitational field must replace the classical Einsteinian picture [7,8,9], especially given a … deep base cabinet drawer for kitchen