Related papers: Extrinsic curvature flows and applications
This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are…
We study a generalized mean curvature flow involving a positive power of the mean curvature and a driving force. In this paper, we first construct all kinds of radially symmetric translating solutions, and then select one of them to satisfy…
This article gathers notes of two lectures given at Grenoble's University in June $2023$, and is an introduction to recent works on shear layers, in collaboration with D. Bian, Y. Guo, T. Nguyen and B. Pausader.
We study the evolution of a Jordan curve on the plane by curvature flow, also known as curve shortening flow, and by level-set flow, which is a weak formulation of curvature flow. We show that the evolution of the curve depends continuously…
I briefly review some of the recent progress in quantum field theory in curved spacetime and other aspects of semiclassical gravity, as reported at the D3 Workshop at GR15.
Researchers have been highly active to investigate the classical machine learning workflow and integrate best practices from the software engineering lifecycle. However, deep learning exhibits deviations that are not yet covered in this…
In this paper, we show how the study of kinematics of a family of trajectories of a classical mechanical system may be unified within the framework of analysis of geodesic flows in Riemannian geometry and Relativity. After setting up the…
Upcoming and planned experiments combining increasingly intense lasers and energetic particle beams will access new regimes of nonlinear, relativistic, quantum effects. This improved experimental capability has driven substantial progress…
This paper agrees basically with the talk of the author at the workshop "Homological Mirror Symmetry and Applications", Institute for Advanced Study, Princeton, March 2007.
We introduce the concept of extrinsic catenary in the hyperbolic plane. Working in the hyperboloid model, we define an extrinsic catenary as the shape of a curve hanging under its weight as seen from the ambient space. In other words, an…
We consider a general formulation of gradient flow evolution for problems whose natural framework is the one of metric spaces. The applications we deal with are concerned with the evolution of {\it capacitary measures} with respect to the…
Hadamard spaces have traditionally played important roles in geometry and geometric group theory. More recently, they have additionally turned out to be a suitable framework for convex analysis, optimization and nonlinear probability…
In this paper, we consider the mean curvature flow of convex hypersurfaces in Euclidean spaces with a general forcing term. We show that the flow may shrink to a point in finite time if the forcing term is small, or exist for all times and…
We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other…
A recent article by the first two authors together with B Andrews and V-M Wheeler considered the so-called `ideal curve flow', a sixth order curvature flow that seeks to deform closed planar curves to curves with least variation of total…
I summarize the highlights of "Cosmic Flows: Towards an Understanding of the Large-scale Structure in the Universe", a workshop held in Victoria, Canada in July 1999.
We demonstrate several techniques to encourage practical uses of neural networks for fluid flow estimation. In the present paper, three perspectives which are remaining challenges for applications of machine learning to fluid dynamics are…
The motion of both internal and surface waves in incompressible fluids under capillary and gravity forces is a major research topic. In particular, we review the derivation of some new models describing the dynamics of gravity-capillary…
The notion of the flow introduced by Kitaev is a manifestly topological formulation of the winding number on a real lattice. First, we show in this paper that the flow is quite useful for practical numerical computations for systems without…
This contribution presents a brief survey of clipping and intersection algorithms in E2 and E3 with a nearly complete list of relevant references. Some algorithms use the projective extension of the Euclidean space and vector-vector…