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Anne Pichon - One of the best experts on this subject based on the ideXlab platform.
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MINIMAL SURFACE SINGULARITIES ARE LIPSCHITZ NORMALLY EMBEDDED
Journal of the London Mathematical Society, 2020Co-Authors: Walter D. Neumann, Helge Møller Pedersen, Anne PichonAbstract:Any germ of a complex analytic Space is equipped with two natural metrics: the outer metric induced by the hermitian metric of the Ambient Space and the inner metric, which is the associated riemannian metric on the germ. These two metrics are in general nonequivalent up to bilipschitz homeo-morphism. We show that minimal surface singularities are Lipschitz normally embedded, i.e., their outer and inner metrics are bilipschitz equivalent, and that they are the only rational surface singularities with this property. The proof is based on a preliminary result which gives a general characterization of Lipschitz normally embedded normal surface singularities.
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Minimal surface singularities are Lipschitz normally embedded
Journal of the London Mathematical Society, 2019Co-Authors: Walter D. Neumann, Helge Møller Pedersen, Anne PichonAbstract:Any germ of a complex analytic Space is equipped with two natural metrics: the {\it outer metric} induced by the hermitian metric of the Ambient Space and the {\it inner metric}, which is the associated riemannian metric on the germ. We show that minimal surface singularities are Lipschitz normally embedded (LNE), i.e., the identity map is a bilipschitz homeomorphism between outer and inner metrics, and that they are the only rational surface singularities with this property.
Adela Mihai - One of the best experts on this subject based on the ideXlab platform.
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chen inequalities for submanifolds of real Space forms with a semi symmetric non metric connection
Canadian Mathematical Bulletin, 2012Co-Authors: Cihan Özgür, Adela MihaiAbstract:In this paper we prove Chen inequalities for submanifolds of real Space forms endowed with a semi-symmetric non-metric connection, i.e., relations between the mean curvature associated with a semi-symmetric non-metric connection, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the Ambient Space. The equality cases are considered.
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CHEN INEQUALITIES FOR SUBMANIFOLDS OF REAL Space FORMS WITH A SEMI-SYMMETRIC METRIC CONNECTION
Taiwanese Journal of Mathematics, 2010Co-Authors: Adela Mihai, Cihan ÖzgürAbstract:In this paper we prove Chen inequalities for submanifolds of real Space forms endowed with a semi-symmetric metric connection, i.e., relations between the mean curvature associated with the semi-symmetric metric connection, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the Ambient Space. The equality cases are considered.
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geometric inequalities for purely real submanifolds in complex Space forms
Results in Mathematics, 2009Co-Authors: Adela MihaiAbstract:As a generalisation of Kaehlerian slant submanifolds in Kaehler manifolds (i.e., proper slant submanifolds with the canonical endomorphism P parallel, ∇P = 0) one considers purely real submanifolds with ∇P = 0. The class of purely real submanifolds with ∇P = 0 also contains totally real submanifolds, in particular Lagrangian submanifolds. We obtain Chen-like inequalities for purely real submanifolds in complex Space forms, i.e., relationships between intrinsic and extrinsic invariants of such submanifolds, involving the scalar curvature and Chen first invariant, respectively, and the squared mean curvature and the holomorphic sectional curvature of the Ambient Space.
Walter D. Neumann - One of the best experts on this subject based on the ideXlab platform.
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MINIMAL SURFACE SINGULARITIES ARE LIPSCHITZ NORMALLY EMBEDDED
Journal of the London Mathematical Society, 2020Co-Authors: Walter D. Neumann, Helge Møller Pedersen, Anne PichonAbstract:Any germ of a complex analytic Space is equipped with two natural metrics: the outer metric induced by the hermitian metric of the Ambient Space and the inner metric, which is the associated riemannian metric on the germ. These two metrics are in general nonequivalent up to bilipschitz homeo-morphism. We show that minimal surface singularities are Lipschitz normally embedded, i.e., their outer and inner metrics are bilipschitz equivalent, and that they are the only rational surface singularities with this property. The proof is based on a preliminary result which gives a general characterization of Lipschitz normally embedded normal surface singularities.
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Minimal surface singularities are Lipschitz normally embedded
Journal of the London Mathematical Society, 2019Co-Authors: Walter D. Neumann, Helge Møller Pedersen, Anne PichonAbstract:Any germ of a complex analytic Space is equipped with two natural metrics: the {\it outer metric} induced by the hermitian metric of the Ambient Space and the {\it inner metric}, which is the associated riemannian metric on the germ. We show that minimal surface singularities are Lipschitz normally embedded (LNE), i.e., the identity map is a bilipschitz homeomorphism between outer and inner metrics, and that they are the only rational surface singularities with this property.
John Man Shun - One of the best experts on this subject based on the ideXlab platform.
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parabolic omori yau maximum principle for mean curvature flow and some applications
Journal of Geometric Analysis, 2018Co-Authors: John Man ShunAbstract:We derive a parabolic version of Omori–Yau maximum principle for a proper mean curvature flow when the Ambient Space has lower bound on $$\ell $$ -sectional curvature. We apply this to show that the image of Gauss map is preserved under a proper mean curvature flow in euclidean Spaces with uniformly bounded second fundamental forms. This generalizes the result of Wang (Math Res Lett 10:287–299, 2003) for compact immersions. We also prove a Omori–Yau maximum principle for properly immersed self-shrinkers, which improves a result in Chen et al. (Ann Glob Anal Geom 46:259–279, 2014).
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parabolic omori yau maximum principle for mean curvature flow and some applications
arXiv: Differential Geometry, 2017Co-Authors: John Man ShunAbstract:We derive a parabolic version of Omori-Yau maximum principle for a proper mean curvature flow when the Ambient Space has lower bound on $\ell$-sectional curvature. We apply this to show that the image of Gauss map is preserved under a proper mean curvature flow in euclidean Spaces with uniform bounded second fundamental forms. This generalizes the result of Wang \cite{Wang} for compact immersions. We also prove a Omori-Yau maximum principle for properly immersed self-shrinkers, which improves a result in \cite{CJQ}.
M Elmizadeh - One of the best experts on this subject based on the ideXlab platform.
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a group theoretical approach to graviton two point function
European Physical Journal C, 2015Co-Authors: S Rahbardehghan, H Pejhan, M ElmizadehAbstract:Respecting the group theoretical approach, it is debated that the theory of linear conformal gravity should be formulated through a tensor field of rank-3 and mixed symmetry (Binegar et al., Phys Rev D 27: 2249, 1983). Pursuing this path, such a field equation was obtained in de Sitter Space (Takook et al., J Math Phys 51:032503, 2010). In the present work, considering the de Sitter Ambient Space notation, a proper solution to the physical part of this field equation is obtained. We have also calculated the related two-point function, which is interestingly de Sitter invariant and free of an infrared divergence.
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a group theoretical approach to graviton two point function
arXiv: General Relativity and Quantum Cosmology, 2014Co-Authors: S Rahbardehghan, H Pejhan, M ElmizadehAbstract:Respecting the group theoretical approach, it is debated that the theory of linear conformal gravity should be formulated through a tensor field of rank-3 and mixed symmetry \cite{binegar}. Pursuing this path, such a field equation was obtained in de Sitter Space \cite{takook}. In present work, considering the de Sitter Ambient Space notation, a proper solution to the physical part of this field equation is obtained. We have also calculated the related two-point function, which is interestingly de Sitter invariant and free of infrared divergence.