Many optimization problems formulated on Riemannian manifolds involve their intrinsic Riemannian squared distance function. A notorious and important example is the centroid computation of a given finite constellation of points. In such setups, the implementation of the fast intrinsic Newton optimization scheme requires the availability of the Hessian of this intrinsic function. Here, a method ...

in this paper, we present an edge detection method based on wavelet transform and hessian matrix of image at each pixel. many methods which based on wavelet transform, use wavelet transform to approximate the gradient of image and detect edges by searching the modulus maximum of gradient vectors. in our scheme, we use wavelet transform to approximate hessian matrix of image at each pixel, too. ...

In recent years, learning on manifolds has attracted much attention in the academia community. The idea that the distribution of real-life data forms a low dimensional manifold embedded in the ambient space works quite well in practice, with applications such as ranking, dimensionality reduction, semi-supervised learning and clustering. This paper focuses on ranking on manifolds. Traditional ma...

Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a non degenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization, which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a fami...

Abstract We construct a family of quasimetric spaces in generalized potential theory containing m -subharmonic functions with finite ( p , )-energy. These will be viewed both $${\mathbb {C}}^n$$ C n and compact Kähler manifolds, their convergence ...

On a compact connected 2m-dimensional Kähler manifold with Kähler form ω, given a smooth function f : M → R and an integer 1 < k < m, we want to solve uniquely in ω the equation ω̃ ∧ωm−k eω, relying on the notion of k-positivity for ω̃ ∈ ω the extreme cases are solved: k m by Yau in 1978 , and k 1 trivially . We solve by the continuity method the corresponding complex elliptic kthHessian equation...

on a Riemannian manifold (M n , g), where f is a symmetric function of λ ∈ R , κ is a constant, ∇2u denotes the Hessian of a function u on M and, for a (0, 2) tensor h on M , λ(h) = (λ1, · · · , λn ) denotes the eigenvalues of h with respect to the metric g. The Dirichlet problem for equations of type (1.1) in R , with κ = 0, under various hypothesis, is studied by Caffarelli, Nirenberg and Spr...

In this article, we derived an equality for CR-warped product in a complex space form which forms the relationship between gradient and Laplacian of warping function second fundamental form. We necessary conditions submanifolds Ka¨hler manifold to be Einstein impact Ricci soliton. Some classification by using Euler–Lagrange equation, Dirichlet energy Hamiltonian is given. also derive some chara...

We define a Hesse soliton, that is, self-similar solution to the flow on Hessian manifolds. On information geometry, e-connection is important, which does not coincide with Levi–Civita one. Therefore, it interesting consider manifold flat connection call proper manifold. In this paper, we show any compact soliton expanding and non-trivial gradient proper. Furthermore, dual space of Hesse–Einste...

In this paper, we prove that, for compact warped product submanifolds Mn in an Euclidean space En+k, there are no stable p-currents, homology groups vanishing, and M3 is homotopic to the sphere S3 under various extrinsic restrictions, involving eigenvalue of function, integral Ricci curvature, Hessian tensor. The results paper can be considered extension Xin’s work framework a submanifold, when...