Results 51 to 60 of about 103,878 (263)
Parabolic Frequency on Ricci Flows
International Mathematics Research Notices, 2022 AbstractThis paper defines a parabolic frequency for solutions of the heat equation on a Ricci flow and proves its monotonicity along the flow. Frequency monotonicity is known to have many useful consequences; here it is shown to provide a simple proof of backwards uniqueness.
Baldauf, Julius, Kim, Dain
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Schizophrenia Genetics Modulates Clinical Depressive Features
American Journal of Medical Genetics Part B: Neuropsychiatric Genetics, EarlyView.ABSTRACT Schizophrenia (SCZ) genetic liability, quantified by polygenic scores (PGS), may influence clinical phenotypes in major depressive disorder (MDD). We investigated the effect of the SCZ‐PGS derived from the latest SCZ genome‐wide association study (GWAS) on MDD symptom severity, comorbidities, and treatment outcomes.
Alessandro Serretti +13 more
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Ricci flow on quasiprojective manifolds II
, 2016 We study the Ricci flow on complete Kaehler metrics that live on the complement of a divisor in a compact complex manifold. In earlier work, we considered finite-volume metrics which, at spatial infinity, are transversely hyperbolic. In the present paper
Lott, John, Zhang, Zhou
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Evolution of a geometric constant along the Ricci flow
Journal of Inequalities and Applications, 2016 In this paper, we establish the first variation formula of the lowest constant λ a b ( g ) $\lambda_{a}^{b}(g)$ along the Ricci flow and the normalized Ricci flow, such that to the following nonlinear equation there exist positive solutions: − Δ u + a u ...
Guangyue Huang, Zhi Li
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Propagation of symmetries for Ricci shrinkers
Advanced Nonlinear Studies, 2023 We will show that if a gradient shrinking Ricci soliton has an approximate symmetry on one scale, this symmetry propagates to larger scales. This is an example of the shrinker principle which roughly states that information radiates outwards for ...
Colding Tobias Holck +1 more
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Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs
Communications on Pure and Applied Mathematics, EarlyView.Abstract We study isoperimetric inequalities on “slabs”, namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension‐one base. As our two main applications, we consider the case when the base is the flat torus R2/2Z2$\mathbb {R}^2 / 2 \mathbb {Z}^2$ and the standard Gaussian measure
Emanuel Milman
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PMC Physics A, 2007 15 pages. V2: improved presentation, in particular Jordan vs. Brans-Dicke and on viability. Added section on physical interpretation. V3: more references.
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Degree theory for 4‐dimensional asymptotically conical gradient expanding solitons
Communications on Pure and Applied Mathematics, EarlyView.Abstract We develop a new degree theory for 4‐dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymptotic to any given cone over S3$S^3$ with non‐negative scalar curvature. We also obtain a similar existence result for cones whose link is diffeomorphic to S3/Γ$S^3/\
Richard H. Bamler, Eric Chen
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The K\"ahler-Ricci flow on Fano manifolds [PDF]
, 2013 In this lecture notes, we aim at giving an introduction to the K\"ahler-Ricci flow (KRF) on Fano manifolds. It covers some of the developments of the KRF in its first twenty years (1984-2003), especially an essentially self-contained exposition of ...
Cao, Huai-Dong
core
Stability of hyperbolic space under Ricci flow
, 2010 We study the Ricci flow of initial metrics which are C^0-perturbations of the hyperbolic metric on H^n. If the perturbation is bounded in the L^2-sense, and small enough in the C^0-sense, then we show the following: In dimensions four and higher, the ...
Schnürer, Oliver C. +2 more
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