2024 Metric inequalities with scalar curvature

Metric inequalities with scalar curvature

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August undefined, 2024

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 … 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 …

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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 … 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 … fruit tree canker disease

Metric Inequalities with Scalar Curvature – arXiv Vanity

Web4 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 … 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 … 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 concerned these inequalities appear as generalisations of the classical bounds on the distances between conjugates points in surfaces with positive sectional curvatures. The techniques … fruit tree collection uk

Metric Inequalities with Scalar Curvature — NYU Scholars

[1710.04655v3] Metric Inequalities with Scalar Curvature

WebIn 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 ... 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 … fruit tree blight treatment denverWeb5 mei 2024 · Going back to the original variables, this implies that holds, concluding the proof.Funding. This work has been done while G.C. was visiting the University of Texas at Austin under the support of NSF FRG Grant DMS-1361122, the Oden Fellowship at ICES, the GNAMPA of the Istituto Nazionale di Alta Matematica (INdAM), and the FIR project … gif grinch

"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

Metric inequalities with scalar curvature

The scalar curvature equation on 2- and 3-spheres SpringerLink

Web4 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. 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”) …

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WebGromov M., Metric inequalities with scalar curvature, Geom. Funct. Anal.28(2024), 645-726, arXiv:1710.04655. Gromov M., Four lectures on scalar curvature, arXiv:1908.10612. Gromov M., Lawson Jr. H.B., Spin and scalar curvature in the presence of a fundamental group. I, Ann. of Math.111(1980), 209-230. 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 …

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 … 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.

Web2 aug. 2024 · According to the linked page on prescribed scalar curvature, by work of Kazdan and Warner, "If the dimension of M is three or greater, then any smooth function … WebMetric Inequalities with Scalar Curvature. Misha Gromov Abstract We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the …

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 …

WebWe establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below. fruit tree farming groupWeb13 apr. 2024 · where \text {Ric}_g and \text {diam}_g, respectively, denote the Ricci tensor and the diameter of g and g runs over all Riemannian metrics on M. By using Kummer-type method, we construct a smooth closed almost Ricci-flat nonspin 5-manifold M which is simply connected. It is minimal volume vanishes; namely, it collapses with sectional … fruit tree farm baldwin nyWeb12 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. gif grocery shoppingWeb21 nov. 2024 · Metric Inequalities with Scalar Curvature M. Gromov Mathematics Geometric and Functional Analysis 2024 We establish several inequalities for manifolds … fruit tree farms near meWeb14 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 ... fruit tree cross pollinationWeb1 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 fruit tree farm osrsWeb12 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 spirit … fruit tree cuttings cheap