Results 11 to 20 of about 4,567,624 (190)
Convergence of the weighted Yamabe flow [PDF]
Differential Geometry and its Applications, 2021 We introduce the weighted Yamabe flow $\frac{\partial g}{\partial t}=(r^m_ϕ-R^m_ϕ)g$, $\frac{\partial ϕ}{\partial t}=\frac{m}{2}(R^m_ϕ-r^m_ϕ)$ on a smooth metric measure space $(M^n, g, e^{-ϕ}{\rm dvol}_g, m)$, where $R^m_ϕ$ denotes the associated weighted scalar curvature, and $r^m_ϕ$ denotes the mean value of the weighted scalar curvature.
Zetian Yan
semanticscholar +5 more sources
CR Yamabe constant, CR Yamabe flow and its soliton [PDF]
Nonlinear Analysis, 2020 To appear in NONLINEAR ANALYSIS-THEORY METHODS & ...
P. Ho, Kunbo Wang
semanticscholar +6 more sources
The Yamabe flow on asymptotically Euclidean manifolds with nonpositive Yamabe constant [PDF]
Journal of Functional Analysis, 2022 We study the Yamabe flow on asymptotically flat manifolds with non-positive Yamabe constant $Y\leq 0$. Previous work by the second and third named authors \cite{ChenWang} showed that while the Yamabe flow always converges in a global weighted sense when $Y>0$, the flow must diverge when $Y\leq 0$.
G. Carron, Eric Chen, Yi Wang
semanticscholar +7 more sources
Conic manifolds under the Yamabe flow [PDF]
Journal of Evolution Equations, 2018 We consider the unnormalized Yamabe flow on manifolds with conical singularities. Under certain geometric assumption on the initial cross section, we show well-posedness of the short-time solution in the $$L^q$$ L q -setting.
N. Roidos
semanticscholar +7 more sources
Yamabe flow: Steady solitons and Type II singularities [PDF]
Nonlinear Analysis, 2017 We study the convergence of complete non-compact conformally flat solutions to the Yamabe flow to Yamabe steady solitons. We also prove the existence of Type II singularities which develop at either a finite time $T$ or as $t \to +\infty$.
Beomjun Choi, P. Daskalopoulos
semanticscholar +6 more sources
The Yamabe flow on asymptotically flat manifolds [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2021 We study the Yamabe flow starting from an asymptotically flat manifold ( M n , g 0 ) (M^{n},g_{0}) . We show that the flow converges to an asymptotically flat, scalar flat metric in a weighted global sense if Y ( M , [ g 0 ] ) > 0 Y(M,[g_{0}])>0 , and ...
Eric Chen, Yi Wang
semanticscholar +4 more sources
Slowly converging Yamabe flows [PDF]
Geometry & Topology, 2015 We characterize the rate of convergence of a converging volume-normalized Yamabe flow in terms of Morse theoretic properties of the limiting metric. If the limiting metric is an integrable critical point for the Yamabe functional (for example, this holds
Carlotto, Alessandro +2 more
core +3 more sources
Evolution of relative Yamabe constant under Ricci Flow [PDF]
, 2019 Let $W$ be a manifold with boundary $M$ given together with a conformal class $\bar C$ which restricts to a conformal class $C$ on $M$. Then the relative Yamabe constant $Y_{\bar C}(W,M;C)$ is well-defined.
Botvinnik, Boris, Lu, Peng
core +5 more sources
The Yamabe flow on incomplete manifolds [PDF]
Journal of Evolution Equations, 2017 This article is concerned with developing an analytic theory for second order nonlinear parabolic equations on singular manifolds. Existence and uniqueness of solutions in an Lp-framework is established by maximal regularity tools.
Shao, Yuanzhen
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Global Yamabe flow on asymptotically flat manifolds [PDF]
, 2021 Li Ma
semanticscholar +3 more sources