1. The Ricci Flow: An Introduction - AMS Bookstore
Intuitively, the idea is to set up a PDE that evolves a metric according to its Ricci curvature. The resulting equation has much in common with the heat ...
The Ricci Flow: An Introduction
2. Nurowski's conformal class of a maximally symmetric (2,3,5)
Mar 24, 2021 · Research ArticleNurowski's Conformal Class of a Maximally Symmetric (2,3,5)-Distribution and its Ricci-flat RepresentativesMatthew ...
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3. Ricci Truong - Facebook
Ricci Truong is on Facebook. Join Facebook to connect with Ricci Truong and others you may know. Facebook gives people the power to share and makes the...
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4. View of Gradient almost Para-Ricci-like Solitons on Para ...
... its Ricci tensorρhas the form [1]ρ=−12Lvg−λg,whereLdenotes the Lie derivative,vis a vector field andλis a constant. Afterits introduction a detailed study ...
5. [2202.00412] Para-Ricci-like solitons with arbitrary potential on ... - arXiv
Feb 1, 2022 · For the studied soliton, it is proved that its Ricci tensor is a constant multiple of the vertical component of both metrics. Thus, the ...
Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian $Π$-manifolds are introduced and studied. For the studied soliton, it is proved that its Ricci tensor is a constant multiple of the vertical component of both metrics. Thus, the corresponding scalar curvatures of both considered metrics are equal and constant. An explicit example of the Lie group as the manifold under study is presented.
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6. View of The Conjugate Linearized Ricci Flow on Closed 3-Manifolds
We also provide an integral representation of the Ricci flow metricitself and of its Ricci tensor in terms of the heat kernel of the conjugate linearized ...
7. Capacity for minimal graphs over manifolds and the half-space property
Jun 27, 2023 · On the other hand, we prove that any M-parabolic end is indeed parabolic provided its Ricci curvature is uniformly bounded from below.
In this paper, we define natural capacities using a relative volume of graphs over manifolds, which can be characterized by solutions of bounded variation to Dirichlet problems of minimal hypersurface equation. Using the capacities, we introduce a notion '$M$-parabolicity' for ends of complete manifolds, where a parabolic end must be $M$-parabolic, but not vice versa in general. We study the boundary behavior of solutions associated with capacities in the measure sense, and the existence of minimal graphs over $M$-parabolic or $M$-nonparabolic manifolds outside compact sets. For a $M$-parabolic manifold $P$, we prove a half-space theorem for complete proper minimal hypersurfaces in $P\times\mathbb{R}$. As a corollary, we immediately have a slice theorem for smooth mean concave domains in $P\times\mathbb{R}^+$, where the $M$-parabolic condition is sharp by our example. On the other hand, we prove that any $M$-parabolic end is indeed parabolic provided its Ricci curvature is uniformly bounded from below. Compared to harmonic functions, we get the asymptotic estimates with sharp orders for minimal graphic functions on nonparabolic manifolds of nonnegative Ricci curvature outside compact sets.
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8. Nurowski's Conformal Class of a Maximally Symmetric (2,3,5)
Dec 10, 2020 · Nurowski's Conformal Class of a Maximally Symmetric (2,3,5)-Distribution and its Ricci-flat Representatives. Authors. Matthew Randall.
We show that the solutions to the second-order differential equation associated to the generalised Chazy equation with parameters k = 2 and k = 3 naturally show up in the conformal rescaling that takes a representative metric in Nurowski’s conformal class associated to a maximally symmetric (2,3,5)-distribution (described locally by a certain function...
9. ITS RICCI by Cheerycide - Fur Affinity
ITS RICCI ; Category Artwork (Digital) / Doodle ; Species Pokemon ; Gender Female ; Size 1160 x 1600px.
The girl, the menace, Ricci Estavez
![ITS RICCI by Cheerycide - Fur Affinity](https://i0.wp.com/t.furaffinity.net/53804775@600-1695654070.jpg)
10. Implementing quantum Ricci curvature - Physical Review Link Manager
May 21, 2018 · ... properties of the underlying quantum geometry, its Ricci curvature can be matched well to that of a five-dimensional round sphere.
Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure. Besides coordinate invariance, its key features are scalability, computability, and robustness. We demonstrate that these properties continue to hold in the context of nonperturbative quantum gravity, by evaluating the quantum Ricci curvature numerically in two-dimensional Euclidean quantum gravity, defined in terms of dynamical triangulations. Despite the well-known, highly nonclassical properties of the underlying quantum geometry, its Ricci curvature can be matched well to that of a five-dimensional round sphere.
11. Geometry & Topology Volume 25, issue 2 (2021)
Abstract. Given a three-dimensional Riemannian manifold containing a ball with an explicit lower bound on its Ricci curvature and positive lower bound on ...
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12. Conical structure for shrinking Ricci solitons - EMS Press
Oct 3, 2017 · Abstract. It is shown that a shrinking gradient Ricci soliton must be smoothly asymptotic to a cone if its Ricci curvature goes to zero at ...
Ovidiu Munteanu, Jiaping Wang
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13. Conical structure for shrinking Ricci solitons - Experts@Minnesota
It is shown that a shrinking gradient Ricci soliton must be smoothly asymptotic to a cone if its Ricci curvature goes to zero at infinity. Original language ...
It is shown that a shrinking gradient Ricci soliton must be smoothly asymptotic to a cone if its Ricci curvature goes to zero at infinity.
14. General Relativity and the Ricci Flow - SciPost Submission
Aug 10, 2021 · In Riemannian geometry, the Ricci flow is the analogue of heat diffusion; a deformation of the metric tensor driven by its Ricci curvature.
SciPost Submission Detail General Relativity and the Ricci Flow
15. A theorem of Yu. A. Aminov - Penn State Research Database
... its Ricci curvature. Original language, English (US). Pages (from-to), 435-437. Number of pages, 3. Journal, Journal of Soviet Mathematics. Volume, 10. Issue ...
We give a simple proof of a somewhat stronger theorem of Yu. A. Aminov concerning a lower estimate of the diameter of a surface immersed in R, this estimate being a function of the mean curvature of the surface and of its Ricci curvature.