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Discrete Yamabe Problem for Polyhedral Surfaces. [PDF]
Discrete Comput Geom, 2023 AbstractWe study a new discretization of the Gaussian curvature for polyhedral surfaces. This discrete Gaussian curvature is defined on each conical singularity of a polyhedral surface as the quotient of the angle defect and the area of the Voronoi cell corresponding to the singularity.
Dal Poz Kouřimská H.
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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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A note on the Yamabe problem of Randers metrics [PDF]
AUT Journal of Mathematics and Computing, 2021 The classical Yamabe problem in Riemannian geometry states that every conformal class contains a metric with constant scalar curvature. In Finsler geometry, the C-convexity is needed in general.
Bin Chen, Siwei Liu
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Kodaira dimension and the Yamabe problem [PDF]
Communications in Analysis and Geometry, 1999 The Yamabe invariant Y(M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unit-volume constant-scalar curvature Riemannian metrics g on M. (To be absolutely precise, one only considers constant-scalar-curvature metrics which are Yamabe minimizers, but this does not affect the sign of the answer.) If M is the underlying ...
Claude LeBrun
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Gradient estimates for a nonlinear elliptic equation on smooth metric measure spaces and applications [PDF]
Heliyon, 2019 In this paper local and global gradient estimates are obtained for positive solutions to the following nonlinear elliptic equationΔfu+p(x)u+q(x)uα=0, on complete smooth metric measure spaces (MN,g,e−fdv) with ∞-Bakry-Émery Ricci tensor bounded from below,
Abimbola Abolarinwa +2 more
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The Yamabe problem with singularities [PDF]
, 2008 Let $(M,g)$ be a compact Riemannian manifold of dimension $n\geq 3$. Under some assumptions, we prove that there exists a positive function $ $ solution of the following Yamabe type equation + h = \tilde h ^{\frac{n+2}{n-2}} where $h\in L^p(M)$, $p>n/2$ and $\tilde h\in \mathbb R$. We give the regularity of $ $ with respect to the value of $
Farid Madani
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On the bifurcation of solutions of the Yamabe problem in product manifolds with minimal boundary [PDF]
Advances in Nonlinear Analysis, 2018 In this paper, we study the multiplicity of solutions of the Yamabe problem on product manifolds with minimal boundary via bifurcation theory.
Cárdenas Diaz Elkin Dario +1 more
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The Yamabe problem on Dirichlet spaces [PDF]
, 2013 We continue our previous work studying critical exponent semilinear elliptic (and subelliptic) problems which generalize the classical Yamabe problem. In [3] the focus was on metric-measure spaces with an `almost smooth' structure, with stratified spaces
Gilles Carron +3 more
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The Yamabe problem on stratified spaces [PDF]
Geometric and Functional Analysis, 2012 44 ...
Kazuo Akutagawa +2 more
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The Yamabe Problem and Nonlinear Boundary Value Problems [PDF]
Journal of Differential Equations, 1995 The paper is concerned with the scalar curvature equation with prescribed mean curvature on the boundary of a given Riemannian manifold. Just as in \textit{T. Ouyang} [Trans. Am. Math. Soc. 331, No. 2, 503-527 (1992; Zbl 0759.35021)], this Riemannian manifold is assumed to have negative constant scalar curvature in the interior and zero mean curvature ...
Kazuaki Taira
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