Results 31 to 40 of about 100 (98)
Microlocal Approach to Tensor Tomography and Boundary and Lens Rigidity [PDF]
, 2008 2000 Mathematics Subject Classification: 53C24, 53C65, 53C21.This is a survey of the recent results by the author and Gunther Uhlmann on the boundary rigidity problem and on the associated tensor tomography problem.Author partly supported by NSF Grant ...
Stefanov, Plamen
core
Some New Characterizations of Trivial Ricci–Bourguignon Solitons
Journal of Mathematics, Volume 2025, Issue 1, 2025.A Ricci–Bourguignon soliton is a self‐similar solution to the Ricci–Bourguignon flow equation, and a Ricci–Bourguignon soliton is called trivial if its potential field is zero or killing. Each trivial Ricci–Bourguignon soliton is an Einstein manifold.
Hana Al-Sodais +5 more
wiley +1 more source
Bakry-Émery Conditions on Almost Smooth Metric Measure Spaces
Analysis and Geometry in Metric Spaces, 2018 In this short note, we give a sufficient condition for almost smooth compact metric measure spaces to satisfy the Bakry-Émery condition BE(K, N). The sufficient condition is satisfied for the glued space of any two (not necessary same dimensional) closed
Honda Shouhei
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Nonlinear Obata type equation on Finsler manifolds without boundary
Open MathematicsWe show that if there is a nonconstant function f ∈ C 1,α (M) satisfying the Obata equation on a Finsler n-manifold (M, F), then (M, F) is isometric to a Finsler n-sphere.
Wang Huarong
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Classification results of Liouville equations and rigidity of Riemannian surfaces
Advanced Nonlinear StudiesWe study the Liouville equation △u + e 2u = 0 in a Riemannian surface (M, g) with nonnegative Ricci curvature. Under some asymptotic lower bound assumptions, we classify all the solutions to this equation, meanwhile we obtain the rigidity results for ...
Ou Qianzhong
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, 1996 . The strong maximum principle is proved to hold for weak (in the sense of support functions) sub- and super-solutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for C 0 spacelike hypersurfaces in a ...
Lars Andersson +5 more
core +1 more source
On minimal hypersurfaces of nonnegatively Ricci curved manifolds
, 1992 International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 3, Page 573-578, 1993.
Yoe Itokawa
wiley +1 more source
α-Mean curvature flow of non-compact complete convex hypersurfaces and the evolution of level sets
Advances in Nonlinear AnalysisWe consider the α\alpha -mean curvature flow for convex graphs in Euclidean space. Given a smooth, complete, strictly convex, non-compact initial hypersurface over a strictly convex projected domain, we derive uniform curvature bounds, which are ...
Kang Hyunsuk, Lee Ki-Ahm, Lee Taehun
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Generic Properties of Critical Points of the Weyl Tensor
Advanced Nonlinear Studies, 2017 Given (M,g)${(M,g)}$, a smooth compact Riemannian n-manifold, we prove that for a generic Riemannian metric g the critical points of the function 𝒲g(ξ):=|Weylg(ξ)|g2${\mathcal{W}_{g}(\xi):=\lvert\mathrm{Weyl}_{g}(\xi)\rvert^{2}_{g}}$ with 𝒲g(ξ)≠0 ...
Micheletti Anna Maria, Pistoia Angela
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Sharp upper bounds for the capacity in the hyperbolic and Euclidean spaces
Advances in Nonlinear AnalysisWe derive various sharp upper bounds for the pp-capacity of a smooth compact set KK in the hyperbolic space Hn{{\mathbb{H}}}^{n} and the Euclidean space Rn{{\mathbb{R}}}^{n}.
Li Haizhong, Li Ruixuan, Xiong Changwei
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