Results 1 to 10 of about 4,522,677 (161)
On the problem of prescribing weighted scalar curvature and the weighted Yamabe flow [PDF]
Analysis and Geometry in Metric Spaces, 2023 The weighted Yamabe problem introduced by Case is the generalization of the Gagliardo-Nirenberg inequalities to smooth metric measure spaces. More precisely, given a smooth metric measure space ( M , g , e − ϕ d V g , m ) \left(M,g,{e}^{-\phi }{\rm{d}}{V}
Pak Tung Ho, Jinwoo Shin
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New type I ancient compact solutions of the Yamabe flow [PDF]
, 2016 We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as t→−∞, to two self-similar complete non-compact solutions to the Yamabe flow moving in opposite directions.
Daskalopoulos, Panagiota +3 more
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3-dimensional combinatorial Yamabe flow in hyperbolic background geometry [PDF]
, 2019 We study the 3-dimensional combinatorial Yamabe flow in hyperbolic background geometry. For a triangulation of a 3-manifold, we prove that if the number of tetrahedra incident to each vertex is at least 23, then there exist real or virtual ball packings ...
Huabin Ge, Bobo Hua
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Long time existence of Yamabe flow on singular spaces with positive Yamabe constant [PDF]
Analysis & PDE, 2023 In this work we establish long-time existence of the normalized Yamabe flow with positive Yamabe constant on a class of manifolds that includes spaces with incomplete cone-edge singularities.
Jørgen Olsen Lye, Boris Vertman
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Perelman's Invariant, Ricci Flow, and the Yamabe Invariants of Smooth Manifolds [PDF]
, 2006 In his study of Ricci flow, Perelman introduced a smooth-manifold invariant called lambda-bar. We show here that, for completely elementary reasons, this invariant simply equals the Yamabe invariant, alias the sigma constant, whenever the latter is non ...
Akutagawa, Kazuo +2 more
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Convergence of the Yamabe flow on singular spaces with positive Yamabe constant [PDF]
Tohoku mathematical journal, 2023 In this work, we study the convergence of the normalized Yamabe flow with positive Yamabe constant on a class of pseudo-manifolds that includes stratified spaces with iterated cone-edge metrics. We establish convergence under a low energy condition.
Gilles Carron +2 more
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First eigenvalues of geometric operators under the Yamabe flow
Annals of Global Analysis and Geometry, 2018 Suppose $(M,g_0)$ is a compact Riemannian manifold without boundary of dimension $n\geq 3$. Using the Yamabe flow, we obtain estimate for the first nonzero eigenvalue of the Laplacian of $g_0$ with negative scalar curvature in terms of the Yamabe metric ...
Ho, Pak Tung
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Slowly converging Yamabe flows [PDF]
, 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
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Normalized Yamabe flow on manifolds with bounded geometry [PDF]
Annals of Global Analysis and Geometry, 2021 The goal of this paper is to study Yamabe flow on a complete Riemannian manifold of bounded geometry with possibly infinite volume. In case of infinite volume, standard volume normalization of the Yamabe flow fails and the flow may not converge. Instead,
Bruno Caldeira +2 more
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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
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