Results 11 to 20 of about 100 (98)
Functional inequalities for the heat flow on time‐dependent metric measure spaces
Journal of the London Mathematical Society, Volume 104, Issue 2, Page 926-955, September 2021., 2021 Abstract We prove that synthetic lower Ricci bounds for metric measure spaces — both in the sense of Bakry–Émery and in the sense of Lott–Sturm–Villani — can be characterized by various functional inequalities including local Poincaré inequalities, local logarithmic Sobolev inequalities, dimension independent Harnack inequality, and logarithmic Harnack
Eva Kopfer, Karl‐Theodor Sturm
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Limits of Riemannian 4‐manifolds and the symplectic geometry of their twistor spaces
Transactions of the London Mathematical Society, Volume 4, Issue 1, Page 100-109, December 2017., 2017 Abstract The twistor space of a Riemannian 4‐manifold carries two almost complex structures, J+ and J−, and a natural closed 2‐form ω. This article studies limits of manifolds for which ω tames either J+ or J−. This amounts to a curvature inequality involving self‐dual Weyl curvature and Ricci curvature, and which is satisfied, for example, by all anti‐
Joel Fine
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Smooth long‐time existence of Harmonic Ricci Flow on surfaces
Journal of the London Mathematical Society, Volume 95, Issue 1, Page 277-304, February 2017., 2017 Abstract We prove that at a finite singular time for the Harmonic Ricci Flow on a surface of positive genus both the energy density of the map component and the curvature of the domain manifold have to blow up simultaneously. As an immediate consequence, we obtain smooth long‐time existence for the Harmonic Ricci Flow with large coupling constant.
Reto Buzano, Melanie Rupflin
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On the geometry of Riemannian manifolds with a Lie structure at infinity
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 4, Page 161-193, 2004., 2004 We study a generalization of the geodesic spray and give conditions for noncomapct manifolds with a Lie structure at infinity to have positive injectivity radius. We also prove that the geometric operators are generated by the given Lie algebra of vector fields.
Bernd Ammann +2 more
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Skew‐symmetric vector fields on a CR‐submanifold of a para‐Kählerian manifold
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 10, Page 535-540, 2004., 2004 We deal with a CR‐submanifold M of a para‐Kählerian manifold M˜, which carries a J‐skew‐symmetric vector field X. It is shown that X defines a global Hamiltonian of the symplectic form Ω on M⊤ and JX is a relative infinitesimal automorphism of Ω. Other geometric properties are given.
Adela Mihai, Radu Rosca
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On the problem of prescribing weighted scalar curvature and the weighted Yamabe flow
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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On the projections of Laplacians under Riemannian submersions
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 1, Page 33-42, 2001., 2001 We give a condition on Riemannian submersions from a Riemannian manifold M to a Riemannian manifold N which will ensure that it induces a differential operator on N from the Laplace‐Beltrami operator on M. Equivalently, this condition ensures that a Riemannian submersion maps Brownian motion to a diffusion.
Huiling Le
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Quaternion CR‐submanifolds of a quaternion Kaehler manifold
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 1, Page 27-37, 2001., 2001 We study the quaternion CR‐submanifolds of a quaternion Kaehler manifold. More specifically we study the properties of the canonical structures and the geometry of the canonical foliations by using the Bott connection and the index of a quaternion CR‐submanifold.
Bassil J. Papantoniou, M. Hasan Shahid
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A characterization of Gromov hyperbolicity of surfaces with variable negative curvature [PDF]
, 2009 18 pages, 4 figures.-- MSC2000 codes: 53C15, 53C21, 53C22, 53C23.MR#: MR2474116 (2009k:53091)Zbl#: Zbl 1153.53320In this paper we show that, in order to check Gromov hyperbolicity of any surface with curvature $K \leq -k^2 < 0$, we just need to verify ...
Tourís, Eva, Portilla, Ana
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Submanifolds of Euclidean space with parallel mean curvature vector
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 3, Page 533-536, 1991., 1990 The object of the paper is to study some compact submanifolds in the Euclidean space Rn whose mean curvature vector is parallel in the normal bundle. First we prove that there does not exist an n‐dimensional compact simply connected totally real submanifold in R2n whose mean curvature vector is parallel.
Tahsin Ghazal, Sharief Deshmukh
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