The comparison geometry of ricci curvature
In 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 pseudo-Euclidean space. WebDec 12, 2014 · The geometry in question involves a particular notion of curvature called the ‘Ricci curvature’. The Ricci curvature arises naturally in many contexts within the world of mathematics, and also in physics, where it appears for example in the theory of relativity. Hamilton showed the Poincaré Conjecture was equivalent to asserting that every ...
The comparison geometry of ricci curvature
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WebGeneralizes the weighted Ricci curvature and develops comparison geometry and geometric analysis in the Finsler context. Offers an accessible entry point to studying … WebFor Riemannian manifolds with a measure we prove mean curvature and volume comparison results when the -Bakry-Emery Ricci tensor is bounded from below and is bounded or is bounded from below, generalizing the classi…
WebThis is an extended version of the talk I gave at the Comparison Geometry Workshop at MSRI in the fall of 1993, giving a relatively up-to-date account of the results and techniques in the comparison geometry of Ricci curvature, an area that has experienced tremendous … WebApr 1, 2024 · We give several Bishop–Gromov relative volume comparisons with integral Ricci curvature which improve the results in Petersen and Wei (Geom Funct Anal 7:1031–1045, 1997).
WebDec 6, 2012 · We prove three new monotonicity formulas for manifolds with a lower Ricci curvature bound and show that they are connected to rate of convergence to tangent cones. In fact, we show that the derivative of each of these three monotone quantities is bounded from below in terms of the Gromov–Hausdorff distance to the nearest cone. WebFor Riemannian manifolds with a measure we prove mean curvature and volume comparison results when the -Bakry-Emery Ricci tensor is bounded from below and is …
WebApr 14, 2024 · The geometry of k-Ricci curvature and a Monge-Ampere equation. Abstract:The k-Ricci curvature interpolates between the Ricci curvature and holomorphic …
WebSep 26, 2024 · Comparison theorems are foundational to our understanding of the geometric features implied by various curvature constraints. This paper considers manifolds with a positive lower bound on either scalar, 2-Ricci, or Ricci curvature, and contains a variety of theorems which provide sharp relationships between this bound and notions of … dick\\u0027s nw sausage and deli in centralia waWebIn 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 … dick\u0027s office supply harlingenWebThis proposal studies the geometry and topology of smooth metric measure spaces with Bakry-Emery Ricci curvature bounded from below and quasi-Einstein metrics. The Bakry-Emery Ricci curvature is an important generalization of Ricci curvature for smooth metric measure space, which occurs naturally as the collapsed measured Gromov-Haudorff limit. city boot london