Curvature A Variational Approach
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Curvature: A Variational Approach
Author: A. Agrachev
language: en
Publisher: American Mathematical Soc.
Release Date: 2019-01-08
The curvature discussed in this paper is a far reaching generalization of the Riemannian sectional curvature. The authors give a unified definition of curvature which applies to a wide class of geometric structures whose geodesics arise from optimal control problems, including Riemannian, sub-Riemannian, Finsler and sub-Finsler spaces. Special attention is paid to the sub-Riemannian (or Carnot–Carathéodory) metric spaces. The authors' construction of curvature is direct and naive, and similar to the original approach of Riemann. In particular, they extract geometric invariants from the asymptotics of the cost of optimal control problems. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.
MUS - Mathematimus - Hyperelliptical Geometry
M.U.S. (Mathematical Uniform Space) is a new number of π (pi), representing the reality of the Universe in which we live. With this number, we created a new geometry, Hyperelliptical Geometry, which will provide the unification of physics, thus uniting the Theory of Relativity and Quantum Theory. A new geometry for a new Mathematics and a new Physics. (ISBN 978-65-00-98107-0).
Scale Space and PDE Methods in Computer Vision
Welcome to the proceedings of the 5th International Conference on Scale-Space and PDE Methods in Computer Vision. The scale-space concept was introduced by Iijima more than 40 years ago and became popular later on through the works of Witkin and Koenderink. It is at the junction of three major schools of thought in image processing and computer vision: the design of ?lters, axiomatic approaches based on partial di?erential equations (PDEs), and variational methods for image regularization. Scale-space ideas belong to the mathematically best-understood approaches in image analysis. They have entered numerous successful applications in medical imaging and a number of other ?elds where they often give results of very high quality. This conference followed biennial meetings held in Utrecht, Corfu, Vancouver and Skye. It took place in a little castle (Schl ̈ osschen Sch ̈ onburg) near the small town of Hofgeismar, Germany. Inspired by the very successful previous meeting at Skye, we kept the style of gathering people in a slightly remote and scenic place in order to encourage many fruitful discussions during the day and in the evening. Wereceived79fullpapersubmissionsofahighstandardthatischaracteristic for the scale-space conferences. Each paper was reviewed by three experts from the Program Committee, sometimes helped by additional reviewers. Based on theresultsofthesereviews,53paperswereaccepted.Weselected24manuscripts for oral presentation and 29 for poster presentation.