By C. T. C. Wall
By C. T. C. Wall
By Alessio Corti
By Alfred S. Posamentier,Robert L. Bannister
By Matthias Heymann
Presenting a examine of geometric motion functionals (i.e., non-negative functionals at the area of unparameterized orientated rectifiable curves), this monograph focuses on the subclass of these functionals whose neighborhood motion is a degenerate kind of Finsler metric which could vanish in yes instructions, taking into account curves with optimistic Euclidean size yet with 0 action. For such functionals, standards are constructed less than which there exists a minimal motion curve prime from one given set to a different. Then the houses of this curve are studied, and the non-existence of minimizers is proven in a few settings.
Applied to a geometrical reformulation of the quasipotential of Wentzell-Freidlin concept (a subfield of enormous deviation theory), those effects can yield the life and homes of utmost probability transition curves among metastable states in a stochastic approach with small noise.
The e-book assumes purely normal wisdom in graduate-level research; all higher-level mathematical suggestions are brought alongside the way.
By Yu.D. Burago,V.A. Zalgaller
A quantity dedicated to the super transparent and intrinsically attractive thought of two-dimensional surfaces in Euclidean areas. the main target is at the connection among the speculation of embedded surfaces and two-dimensional Riemannian geometry, and the impression of homes of intrinsic metrics at the geometry of surfaces.
By Sylvestre Gallot,Dominique Hulin,Jacques Lafontaine
This e-book covers the themes of differential manifolds, Riemannian metrics, connections, geodesics and curvature, with precise emphasis at the intrinsic good points of the topic. It treats intimately classical effects at the kinfolk among curvature and topology. The publication good points a variety of workouts with complete ideas and a sequence of precise examples are picked up many times to demonstrate each one new definition or estate introduced.
By Antoni A. Kosinski
By Liviu Nicolaescu
This self-contained remedy of Morse concept makes a speciality of functions and is meant for a graduate direction on differential or algebraic topology, and also will be of curiosity to researchers. This is the 1st textbook to incorporate themes reminiscent of Morse-Smale flows, Floer homology, min-max thought, second maps and equivariant cohomology, and intricate Morse theory. The reader is anticipated to have a few familiarity with cohomology idea and differential and essential calculus on soft manifolds.
Some positive aspects of the second one variation comprise additional functions, equivalent to Morse concept and the curvature of knots, the cohomology of the moduli house of planar polygons, and the Duistermaat-Heckman formulation. the second one version additionally contains a new bankruptcy on Morse-Smale flows and Whitney stratifications, many new workouts, and numerous corrections from the 1st edition.