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−ϕdVg,m)\left(M,g,{e}^{-\phi }{\rm{d}}{V}_{g},m), the ...
Ho Pak Tung, Shin Jinwoo
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The Yamabe Flow Under the Rotational Ansatz of Noncompact (Pseudo-Riemannian) Solitons: Schwarzschild Solitons and Generalized-Schwarzschild Ones [PDF]
AxiomsThe present paper is aimed at studying the convergence of the Yamabe flow in the case of noncompact solitons. The more specified example of locally conformally flat noncompact solitons is addressed with the aim to newly analyse the qualities of the Ricci
Orchidea Maria Lecian
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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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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 ...
Pak Tung Ho
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Convergence of the Yamabe flow on singular spaces with positive Yamabe constant [PDF]
Tohoku Mathematical Journal, 2023 Gilles Carron, Boris Vertman
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Yamabe flow: Steady solitons and Type II singularities [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2018 Panagiota Daskalopoulos
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Evolution for First Eigenvalue of LT,f on an Evolving Riemannian Manifold
Mathematics, 2022 In this paper, evolution formulas for the first non-zero eigenvalue of the operator LT,f on a weighted closed Riemannian manifold along the Ricci flow as well as along the Yamabe flow are formulated.
Apurba Saha +4 more
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On The Existence of Yamabe Gradient Solitons [PDF]
International Journal of Mathematical, Engineering and Management Sciences, 2018 The Yamabe soliton is a special soliton of Yamabe flow obtained by R. S. Hamilton, which was formulated due to Yamabe formula introduced by H. Yamabe in 1960. Recently Cao, Sun and Zhang introduced Yamabe gradient soliton. In this paper, the existence of
Yadab Chandra Mandal, Shyamal Kumar Hui
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FIRST EIGENVALUES OF GEOMETRIC OPERATORS UNDER THE YAMABE FLOW
Bulletin of the Korean Mathematical Society, 2016 Shouwen Fang
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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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