Related papers: Gradient Flow on Finsler manifold
Some general Finsler connections are defined. Emphasis is being made on the Cartan tensor and its derivatives. Vanishing of the hv-curvature tensors of these connections characterizes Landsbergian, Berwaldian as well as Riemannian…
In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.
In this article a relation between curvature functionals for surfaces in the Euclidean space and area functionals in relative differential geometry will be given. Relative differential geometry can be described as the geometry of surfaces…
Dense granular flows exhibit both surface deformation and secondary flows due to the presence of normal stress differences. Yet, a complete mathematical modelling of these two features is still lacking. This paper focuses on a steady…
We consider the geometric evolution of a network in the plane, flowing by anisotropic curvature. We discuss local existence of a classical solution in the presence of several smooth anisotropies. Next, we discuss some aspects of the…
The present paper is devoted to the investigation of absolutely continuous curves in asymmetric metric spaces induced by Finsler structures. Firstly, for asymmetric spaces induced by Finsler manifolds, we show that three different kinds of…
We introduce a geometric approach of integral curves for functional inequalities involving directional derivatives in the general context of differentiable manifolds that are equipped with a volume form. We focus on Hardy-type inequalities…
In this paper, we introduce a framework of $(\alpha,\beta)$-flows on triangulated manifolds with two and three dimensions, which unifies several discrete curvature flows previously defined in the literature.
We develop a geometric flow framework to investigate two classical shape functionals: the torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. First, by constructing novel deformation paths governed by height-stretching…
This paper describes the foundations of a differential geometry of a quaternionic curves. The Frenet-Serret equations and the evolutes and evolvents of a particular quaternionic curve are accordingly determined. This new formulation takes…
A geodesic circle in Finsler geometry is a natural extension of that in a Euclidean space. In this paper, we apply Lie derivatives and the Cartan $Y$-connection to study geodesic circles and (infinitesimal) concircular transformations on a…
We discuss conformal deformation and warped products on some open manifolds. We discuss how these can be applied to construct Riemannian metrics with specific scalar curvature functions.
This article is concerned with the existence of nonnegative weak solutions to a particular fourth-order partial differential equation: it is a formal gradient flow with respect to a generalized Wasserstein transportation distance with…
We classify global surfaces of section for flows on 3-manifolds defining Seifert fibrations. We discuss branched coverings -- one way or the other -- between surfaces of section for the Hopf flow and those for any other Seifert fibration of…
This is an introduction to the subject of the differential topology of the space of smooth loops in a finite dimensional manifold. It began as the background notes to a series of seminars given at NTNU and subsequently at Sheffield. I am…
The geometry on a slope of a mountain is the geometry of a Finsler metric, called here the {\it slope metric}. We study the existence of globally defined slope metrics on surfaces of revolution as well as the geodesic's behavior. A…
In this paper, I describe the construction of certain functional integrals in the gradient on finitely ramified fractals, which have a sort of self-similarity property.
Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities…
This is a survey of some of the recent developments on the geometric and analytic aspects of the Anomaly flow. It is a flow of $(2,2)$-forms on a $3$-fold which was originally motivated by string theory and the need to preserve the…
Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allow optimization of their parameters to be efficiently performed via maximum likelihood. However, data of interest are typically assumed to live…