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Longer titles found: Prescribed Ricci curvature problem (view), Milnor conjecture (Ricci curvature) (view)

searching for Ricci curvature 42 found (234 total)

Guofang Wei (677 words) [view diff] exact match in snippet view article find links to article

manifolds with nonnegative Ricci curvature, she has completed work on the isometry groups of manifolds with negative Ricci curvature with coauthors Xianzhe

Oswald Veblen Prize in Geometry (1,819 words) [view diff] exact match in snippet view article find links to article

Proc. Natl. Acad. Sci. U.S.A. 74 (1977), no. 5, 1798–1799. On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation

Quaternion-Kähler symmetric space (264 words) [view diff] exact match in snippet view article find links to article

symmetric space. Any quaternion-Kähler symmetric space with positive Ricci curvature is compact and simply connected, and is a Riemannian product of quaternion-Kähler

Calabi–Yau manifold (3,270 words) [view diff] exact match in snippet view article find links to article

Chern class. M {\displaystyle M} has a Kähler metric with vanishing Ricci curvature. M {\displaystyle M} has a Kähler metric with local holonomy contained

Jeff Cheeger (957 words) [view diff] exact match in snippet view article find links to article

and Functional Analysis. 9 (1999), no. 3, 428–517. Lower bounds on Ricci curvature and the almost rigidity of warped products, with T. H. Colding. Annals

Quaternion-Kähler manifold (1,448 words) [view diff] exact match in snippet view article find links to article

quaternion-Kähler manifolds can thus be naturally divided into those for which the Ricci curvature is positive, and those for which it is instead negative. There are

Tian Gang (3,114 words) [view diff] exact match in snippet view article find links to article

Mathematical Society. 60 (4): 480–483. April 2013. Anderson, Michael T. Ricci curvature bounds and Einstein metrics on compact manifolds. J. Amer. Math. Soc

Richard Schoen (3,287 words) [view diff] exact match in snippet view article find links to article

noncompact manifolds do not admit any complete metrics of nonnegative Ricci curvature. In two papers from the 1980s, Schoen and Karen Uhlenbeck made a foundational

Richard Schoen (3,287 words) [view diff] exact match in snippet view article find links to article

noncompact manifolds do not admit any complete metrics of nonnegative Ricci curvature. In two papers from the 1980s, Schoen and Karen Uhlenbeck made a foundational

Karl-Theodor Sturm (794 words) [view diff] exact match in snippet view article find links to article

Advanced Grant for his research project "Metric measure spaces and Ricci curvature – analytic, geometric, and probabilistic challenges". In 2021, he was

Poincaré conjecture (5,328 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \partial _{t}g_{ij}=-2R_{ij}} where g is the metric and R its Ricci curvature, and one hopes that, as the time t increases, the manifold becomes

Almgren–Pitts min-max theory (811 words) [view diff] exact match in snippet view article find links to article

positive Ricci curvature" (PDF). Arvix.org. Retrieved 2015-05-31. Stephane Sabourau. "Volume of minimal hypersurfaces in manifolds with nonnegative Ricci curvature"

Fake projective plane (1,480 words) [view diff] exact match in snippet view article find links to article

Aubin and Yau on solution of Calabi Conjecture in the case of negative Ricci curvature, see Yau (1977, 1978), any fake projective plane is the quotient of

David Allen Hoffman (541 words) [view diff] exact match in snippet view article find links to article

"Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature". Annals of Mathematics. Second Series. 116 (3): 621–659. doi:10.2307/2007026

Huai-Dong Cao (1,736 words) [view diff] exact match in snippet view article find links to article

Three-manifolds with positive Ricci curvature. Journal of Differential Geometry 17 (1982), no. 2, 255–306. Yau, Shing Tung. On the Ricci curvature of a compact Kähler

De Sitter–Schwarzschild metric (1,783 words) [view diff] exact match in snippet view article find links to article

flat space to measure it relative to. The non-zero components of the Ricci curvature tensor for the de Sitter–Schwarzschild metric are R t t = 1 2 f ( r

Abbas Bahri (450 words) [view diff] case mismatch in snippet view article find links to article

Iskander A. (July 1998). "Periodic Orbits in Magnetic Fields and Ricci Curvature of Lagrangian Systems" (PDF). Transactions of the American Mathematical

Gerhard Huisken (2,224 words) [view diff] exact match in snippet view article find links to article

arbitrary dimensions, in which Hamilton's assumption of the positivity of Ricci curvature is replaced by a quantitative closeness to constant curvature.[H85]

Fano variety (1,249 words) [view diff] exact match in snippet view article find links to article

conjecture, a smooth complex variety admits Kähler metrics of positive Ricci curvature if and only if it is Fano. Myers' theorem therefore tells us that the

Screened Poisson equation (1,331 words) [view diff] exact match in snippet view article find links to article

screened Poisson equation. Under specific conditions, the manifold size, Ricci curvature, and screening parameter are interconnected via a quadratic relationship

Paul C. Yang (388 words) [view diff] exact match in snippet view article find links to article

Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature. Ann. of Math. (2) 155 (2002), no. 3, 709–787. Yang, Paul C.; Yau,

Sun-Yung Alice Chang (1,020 words) [view diff] exact match in snippet view article find links to article

Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature. Ann. of Math. (2) 155 (2002), no. 3, 709–787. Chang, S.-Y. A.; Wilson

Manfredo do Carmo (1,732 words) [view diff] exact match in snippet view article find links to article

ISSN 0273-0979. do Carmo, Manfredo; Xia, Changyu (2000-02-01). "Ricci curvature and the topology of open manifolds". Mathematische Annalen. 316 (2):

Gábor Székelyhidi (486 words) [view diff] exact match in snippet view article find links to article

Székelyhidi, Gábor (17 August 2010). "Greatest lower bounds on the Ricci curvature of Fano manifolds". Compositio Mathematica. 147 (1). Wiley: 319–331

Leon Simon (1,935 words) [view diff] exact match in snippet view article find links to article

"Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature". Annals of Mathematics. Second Series. 116 (3): 621–659. doi:10.2307/2007026

Wanxiong Shi (1,041 words) [view diff] exact match in snippet view article find links to article

Wan-Xiong (1989). "Complete noncompact three-manifolds with non-negative Ricci curvature". J. Differ. Geom. 29 (2): 353–360. doi:10.4310/jdg/1214442879. Shi

Bogomolov–Miyaoka–Yau inequality (1,151 words) [view diff] exact match in snippet view article find links to article

MR 0451180, PMC 431004, PMID 16592394 Yau, Shing Tung (1978), "On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation

String group (1,136 words) [view diff] exact match in snippet view article find links to article

1093/imrn/rns154 Stolz, Stephan (1996), "A conjecture concerning positive Ricci curvature and the Witten genus", Mathematische Annalen, 304 (4): 785–800, doi:10

William Hamilton Meeks, III (807 words) [view diff] exact match in snippet view article find links to article

"Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature". Ann. of Math. 116 (3): 621–659. doi:10.2307/2007026. JSTOR 2007026

Mean curvature flow (2,013 words) [view diff] exact match in snippet view article find links to article

4310/jdg/1214439902. Hamilton, Richard S. (1982). "Three-manifolds with positive Ricci curvature". Journal of Differential Geometry. 17 (2): 255–306. doi:10.4310/jdg/1214436922

Friedmann equations (3,523 words) [view diff] exact match in snippet view article find links to article

time-slice of the universe; it is equal to one-sixth of the spatial Ricci curvature scalar R since R = 6 c 2 a 2 ( a ¨ a + a ˙ 2 + k c 2 ) {\displaystyle

Exact solutions in general relativity (3,323 words) [view diff] exact match in snippet view article find links to article

non-gravitational energy–momentum causes a proportional amount of Ricci curvature "here and now". Moreover, taking covariant derivatives of the field

Derivation of the Schwarzschild solution (3,711 words) [view diff] exact match in snippet view article find links to article

used to set off the index that is being used for the derivative. The Ricci curvature is diagonal in the given coordinates: R t t = − 1 4 B ′ A ( A ′ A −

Inhomogeneous cosmology (2,962 words) [view diff] exact match in snippet view article find links to article

explanation needed], leading to the kinematical backreaction and mean 3-Ricci curvature functionals. Buchert's equations are the main equations[further explanation

Gurzadyan-Savvidy relaxation (1,526 words) [view diff] exact match in snippet view article find links to article

geometric approach Gurzadyan and Armen Kocharyan had introduced the Ricci curvature criterion for relative instability (chaos) of dynamical systems. GS-time

Leroy P. Steele Prize (2,236 words) [view diff] exact match in snippet view article find links to article

2009 Richard S. Hamilton for his paper "Three-manifolds with positive Ricci curvature," J. Differential Geom. 17 (1982), 255-306. 2008 Endre Szemerédi for

Causal sets (5,403 words) [view diff] exact match in snippet view article find links to article

analogue for the d'Alembertian, which can in turn be used to define the Ricci curvature scalar and thereby the Benincasa–Dowker action on a causal set. Monte-Carlo

CR manifold (5,615 words) [view diff] exact match in snippet view article find links to article

connection and torsion and related curvature tensors for example the Ricci curvature and scalar curvature using this metric. This gives rise to an analogous

Vaidya metric (3,476 words) [view diff] exact match in snippet view article find links to article

metric Eq(6), the Ricci tensor has only one nonzero component while the Ricci curvature scalar vanishes, R = g a b R a b = 0 {\displaystyle R=g^{ab}R_{ab}=0}

Bianchi classification (6,581 words) [view diff] exact match in snippet view article find links to article

a ) d x i {\displaystyle \xi _{i}^{(a)}dx^{i}} 　are 1-forms), the Ricci curvature tensor R i k {\displaystyle R_{ik}} is given by: R i k = R ( a ) (

K-stability (8,333 words) [view diff] exact match in snippet view article find links to article

PMC 431004. PMID 16592394. S2CID 9401039. Yau, Shing-Tung (1978). "On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation

List of women in mathematics (22,943 words) [view diff] exact match in snippet view article find links to article

American researcher on Riemannian geometry, metric geometry, and Ricci curvature Vera T. Sós (1930–2023), Hungarian number theorist and combinatorialist