The Experts below are selected from a list of 5298 Experts worldwide ranked by ideXlab platform

Shinichi Ohta - One of the best experts on this subject based on the ideXlab platform.

  • Convexities of metric spaces
    2020
    Co-Authors: Shinichi Ohta
    Abstract:

    Abstract We introduce the k-convexity and the L-convexity of a metric space as generalizations of the CAT(0)-property and of the nonpositively curved property in the sense of Busemann, respectively. Some Banach spaces and CAT(1)-spaces with small diameters satisfy these convexities. We prove the First Variation Formula on a k-convex and L-convex metric space, and extend some known results, including the Dirichlet problem, on the Cheeger-type Sobolev spaces

  • First Variation Formula in wasserstein spaces over compact alexandrov spaces
    Canadian Mathematical Bulletin, 2012
    Co-Authors: Nicola Gigli, Shinichi Ohta
    Abstract:

    We extend results proven by the second author (Amer. J. Math., 2009) for nonnegatively curved Alexandrov spaces to general compact Alexandrov spaces X with curvature bounded below: the gradient flow of a geodesically convex functional on the quadratic Wasserstein space (P(X), W2) satisfies the evolution Variational inequality. Moreover, the gradient flow enjoys uniqueness and contractivity. These results are obtained by proving a First Variation Formula for the Wasserstein distance.

Manuel Barros - One of the best experts on this subject based on the ideXlab platform.

  • Willmore-Like Tori in Killing Submersions
    Advances in Mathematical Physics, 2018
    Co-Authors: Manuel Barros, Oscar J Garay, Álvaro Pámpano
    Abstract:

    The First Variation Formula and Euler-Lagrange equations for Willmore-like surfaces in Riemannian 3-spaces with potential are computed and, then, applied to the study of invariant Willmore-like tori with invariant potential in the total space of a Killing submersion. A connection with generalized elastica in the base surface of the Killing submersion is found, which is exploited to analyze Willmore tori in Killing submersions and to construct foliations of Killing submersions made up of Willmore tori with constant mean curvature.

  • critical curves for the total normal curvature in surfaces of 3 dimensional space forms
    Journal of Mathematical Analysis and Applications, 2012
    Co-Authors: Manuel Barros, Oscar J Garay
    Abstract:

    Abstract A Variational problem closely related to the bending energy of curves contained in surfaces of real 3-dimensional space forms is considered. We seek curves in a surface which are critical for the total normal curvature energy (and its generalizations). We start by deriving the First Variation Formula and the corresponding Euler–Lagrange equations of these energies and apply them to study critical special curves (geodesics, asymptotic lines, lines of curvature) on surfaces. Then, we show that a rotation surface in a real space form for which every parallel is a critical curve must be a special type of a linear Weingarten surface. Finally, we give some classification and existence results for this family of rotation surfaces.

Oscar J Garay - One of the best experts on this subject based on the ideXlab platform.

  • Willmore-Like Tori in Killing Submersions
    Advances in Mathematical Physics, 2018
    Co-Authors: Manuel Barros, Oscar J Garay, Álvaro Pámpano
    Abstract:

    The First Variation Formula and Euler-Lagrange equations for Willmore-like surfaces in Riemannian 3-spaces with potential are computed and, then, applied to the study of invariant Willmore-like tori with invariant potential in the total space of a Killing submersion. A connection with generalized elastica in the base surface of the Killing submersion is found, which is exploited to analyze Willmore tori in Killing submersions and to construct foliations of Killing submersions made up of Willmore tori with constant mean curvature.

  • critical curves for the total normal curvature in surfaces of 3 dimensional space forms
    Journal of Mathematical Analysis and Applications, 2012
    Co-Authors: Manuel Barros, Oscar J Garay
    Abstract:

    Abstract A Variational problem closely related to the bending energy of curves contained in surfaces of real 3-dimensional space forms is considered. We seek curves in a surface which are critical for the total normal curvature energy (and its generalizations). We start by deriving the First Variation Formula and the corresponding Euler–Lagrange equations of these energies and apply them to study critical special curves (geodesics, asymptotic lines, lines of curvature) on surfaces. Then, we show that a rotation surface in a real space form for which every parallel is a critical curve must be a special type of a linear Weingarten surface. Finally, we give some classification and existence results for this family of rotation surfaces.

Nicola Gigli - One of the best experts on this subject based on the ideXlab platform.

  • First Variation Formula in wasserstein spaces over compact alexandrov spaces
    Canadian Mathematical Bulletin, 2012
    Co-Authors: Nicola Gigli, Shinichi Ohta
    Abstract:

    We extend results proven by the second author (Amer. J. Math., 2009) for nonnegatively curved Alexandrov spaces to general compact Alexandrov spaces X with curvature bounded below: the gradient flow of a geodesically convex functional on the quadratic Wasserstein space (P(X), W2) satisfies the evolution Variational inequality. Moreover, the gradient flow enjoys uniqueness and contractivity. These results are obtained by proving a First Variation Formula for the Wasserstein distance.

Toshiyuki Ichiyama - One of the best experts on this subject based on the ideXlab platform.