A survey on positive scalar curvature metrics
From MaRDI portal
Publication:2024154
DOI10.1007/s40574-020-00228-7zbMath1465.53003OpenAlexW3030436058MaRDI QIDQ2024154
Publication date: 3 May 2021
Published in: Bollettino dell'Unione Matematica Italiana (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s40574-020-00228-7
Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Global Riemannian geometry, including pinching (53C20) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02) Homotopy and topological questions for infinite-dimensional manifolds (58B05)
Related Items
The general relativistic constraint equations ⋮ Constrained deformations of positive scalar curvature metrics, II ⋮ A note about isotopy and concordance of positive scalar curvature metrics on compact manifolds with boundary
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Localizing solutions of the Einstein constraint equations
- On the positive mass theorem for manifolds with corners
- Deforming three-manifolds with positive scalar curvature
- The space of metrics of positive scalar curvature
- A proof of the Smale conjecture, \(Diff(S^ 3)\simeq O(4)\)
- Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
- Motion of level sets by mean curvature. I
- Homotopy groups of the moduli space of metrics of positive scalar curvature
- Equivariant Ricci flow with surgery and applications to finite group actions on geometric 3-manifolds
- Conformal deformation of a Riemannian metric to constant scalar curvature
- The existence of negatively Ricci curved metrics on three manifolds
- Riemannian metrics of positive scalar curvature on compact manifolds with boundary
- On the structure of manifolds with positive scalar curvature
- Riemannian geometry as determined by the volumes of small geodesic balls
- Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature
- Spin and scalar curvature in the presence of a fundamental group. I
- The classification of simply connected manifolds of positive scalar curvature
- The space of negative scalar curvature metrics
- Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures
- On the proof of the positive mass conjecture in general relativity
- Kodaira dimension and the Yamabe problem
- Scalar curvature and hammocks
- A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture
- An obstruction to smooth isotopy in dimension \(4\)
- Singular Ricci flows. I
- Three-manifolds with positive Ricci curvature
- Harmonic spinors
- On the scalar curvature of complex surfaces
- The Seiberg-Witten invariants and symplectic forms
- On Galois covers of Hirzebruch surfaces
- The space of positive scalar curvature metrics on a manifold with boundary
- Simply connected manifolds of positive scalar curvature
- Infinite loop spaces and positive scalar curvature
- Positive scalar curvature with skeleton singularities
- Sur les difféomorphismes de la sphère de dimension trois \(\Gamma_ 4 = 0\)
- Global aspects of the Cauchy problem in general relativity
- Complete minimal surfaces in \(S^ 3\)
- Métriques riemanniennes et courbure
- On compact conformally euclidean spaces of dimension \(>2\)
- On conformally-flat spaces in the large
- Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires
- Some sharp isoperimetric theorems for Riemannian manifolds
- A Dozen Problems, Questions and Conjectures About Positive Scalar Curvature
- Nonconnected Moduli Spaces of Positive Sectional Curvature Metrics
- Moduli spaces of invariant metrics of positive scalar curvature on quasitoric manifolds
- On the Bartnik mass of apparent horizons
- The Yamabe problem
- Construction of Manifolds of Positive Scalar Curvature
- A Unique Decomposition Theorem for 3-Manifolds
- Sharp local isoperimetric inequalities involving the scalar curvature
- Metrics of Positive Scalar Curvature on Spherical Space Forms
- The topology of positive scalar curvature
- Diffeomorphisms of the 2-Sphere
- The Weyl and Minkowski problems in differential geometry in the large
- Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations