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The Yamabe invariant (Q5003449)

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scientific article; zbMATH DE number 7373647

Language	Label	Description	Also known as
English	The Yamabe invariant	scientific article; zbMATH DE number 7373647

Statements

scholarly article

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The Yamabe invariant (English)

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zbMATH Open document ID

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10.1090/suga/456

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Kazuo Akutagawa

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Sugaku Expositions

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publication date

22 July 2021

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

Yamabe problem

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Einstein-Hilbert functional

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4-dimensional manifolds

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Riemannian orbifolds

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1090/suga/456

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Yamabe metrics of positive scalar curvature and conformally flat manifolds

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An obstruction to the positivity of relative Yamabe invariants

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Computations of the orbifold Yamabe invariant

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Aubin's lemma for the Yamabe constants of infinite coverings and a positive mass theorem

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The relative Yamabe invariant

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Manifolds of positive scalar curvature and conformal cobordism theory

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Yamabe metrics on cylindrical manifolds

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The Yamabe invariants of orbifolds and cylindrical manifolds, and L[2]-harmonic spinors

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The Weyl functional near the Yamabe invariant

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The Yamabe problem on stratified spaces

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Hölder regularity of solutions for Schrödinger operators on stratified spaces

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The Yamabe problem on Dirichlet spaces

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On Yamabe constants of Riemannian products

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Perelman's invariant, Ricci flow, and the Yamabe invariants of smooth manifolds

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3-manifolds with Yamabe invariant greater than that of \(\mathbb R \mathbb P^3\)

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The signature package on Witt spaces

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Smooth Yamabe invariant and surgery

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The conformal Yamabe constant of product manifolds

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Square-integrability of solutions of the Yamabe equation

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Low-dimensional surgery and the Yamabe invariant

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Ricci Curvature Bounds and Einstein Metrics on Compact Manifolds

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Orbifold compactness for spaces of Riemannian metrics and applications

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Canonical metrics on 3-manifolds and 4-manifolds

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Curvature, cones and characteristic numbers

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Problèmes isoperimetriques et espaces de Sobolev

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Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire

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On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth

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The mass of an asymptotically flat manifold

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A stable cohomotopy refinement of Seiberg-Witten invariants. I

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Einstein manifolds

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The hyperbolic manifolds are local minima of the topological entropy

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A variational approach for compact homogeneous Einstein manifolds

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Manifolds with positive curvature operators are space forms

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Proof of the Riemannian Penrose inequality using the positive mass theorem.

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Classification of prime 3-manifolds with \(\sigma\) invariant greater than \(\mathbb RP^3\)

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Blow-up phenomena for the Yamabe equation

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Blow-up phenomena for the Yamabe equation. II

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Recent progress on the Yamabe problem

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Manifolds with 1/4-pinched curvature are space forms

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Homotopy groups of the moduli space of metrics of positive scalar curvature

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A Relation Between Pointwise Convergence of Functions and Convergence of Functionals

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An a priori estimate for a fully nonlinear equation on four-manifolds.

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On conformally Kähler, Einstein manifolds

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Problèmes de Neumann non linéaires sur les variétés riemanniennes

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Harmonic Mappings of Riemannian Manifolds

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A negative answer to a conjecture of conformal transformations of Riemannian manifolds

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The Yamabe problem on manifolds with boundary

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The classification of simply connected manifolds of positive scalar curvature

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Positive scalar curvature and the Dirac operator on complete Riemannian manifolds

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Yamabe invariants and \(\text{spin}^c\) structures

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Volume comparison and the \(\sigma_k\)-Yamabe problem

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Three-manifolds with positive Ricci curvature

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Harmonic spinors

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On Yamabe constants of products with hyperbolic spaces

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The inverse mean curvature flow and the Riemannian Penrose inequality

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Relative Yamabe invariant and \(c\)-concordant metrics

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Constantes explicites pour les inégalités de Sobolev sur les variétés Riemanniennes compactes

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On the conformal transformation group of a compact Riemannian manifold with constant scalar curvature

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Spin manifolds, Einstein metrics, and differential topology

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Curvature, connected sums, and Seiberg-Witten theory

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Yamabe invariants and the \(\mathrm{Pin}^-(2)\)-monopole equations

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Conformal deformations of conic metrics to constant scalar curvature

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Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures

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Scalar curvature and conformal deformation of Riemannian structure

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A compactness theorem for the Yamabe problem

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Notes on Perelman's papers

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On a conformally invariant functional of the space of Riemannian metrics

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Scalar curvature of a metric with unit volume

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Scalar curvature of spheres

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Yamabe metrics and conformal transformations

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A remark on the Ricci curvature of algebraic surfaces of general type

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The construction of ALE spaces as hyper-Kähler quotients

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Einstein metrics and Mostow rigidity

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Four-manifolds without Einstein metrics

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Yamabe constants and the perturbed Seiberg-Witten equations

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Kodaira dimension and the Yamabe problem

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Ricci curvature, minimal volumes, and Seiberg-Witten theory

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The Yamabe problem

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The prescribed scalar curvature problem for metrics with unit total volume

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Deforming three-manifolds with positive scalar curvature

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Elliptic theory of differential edge operators I

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The local Yamabe constant of Einstein stratified spaces

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An Obata singular theorem for stratified spaces

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The conjectures on conformal transformations of Riemannian manifolds

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On Witten's proof of the positive energy theorem

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The isoperimetric problem in spherical cylinders

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Computations of the Yamabe invariant

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The Yamabe invariant of simply connected manifolds

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Isoperimetric regions in spherical cones and Yamabe constants of \(M \times S^{1}\)

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Isoperimetric profile comparisons and Yamabe constants

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On the Yamabe constants of \(S^2\times\mathbb R^3\) and \(S^3\times\mathbb R^2\)

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Surgery and the Yamabe invariant

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Riemannian Geometry

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Conformal deformation of a Riemannian metric to constant scalar curvature

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On the proof of the positive mass conjecture in general relativity

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Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature

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On the structure of manifolds with positive scalar curvature

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Conformally flat manifolds, Kleinian groups and scalar curvature

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Simply connected manifolds of positive scalar curvature

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Surgery, Yamabe invariant, and Seiberg-Witten theory

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Best constant in Sobolev inequality

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Three dimensional manifolds, Kleinian groups and hyperbolic geometry

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Bach-flat asymptotically locally Euclidean metrics

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Moduli spaces of critical Riemannian metrics in dimension four

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Estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds

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Monopole metrics and the orbifold Yamabe problem

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Einstein metrics and Yamabe invariants of weighted projective spaces

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Metrics of positive scalar curvature and generalised Morse functions, part I

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A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities

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A new proof of the positive energy theorem.

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Monopoles and four-manifolds

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Mathematics(1 entry)

mardi Publication:5003449

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