Nonsmooth Differential Geometry-An Approach Tailored for Spaces with Ricci Curvature Bounded from Below - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonsmooth Differential Geometry-An Approach Tailored for Spaces with Ricci Curvature Bounded from Below write by Nicola Gigli. This book was released on 2018-02-23. Nonsmooth Differential Geometry-An Approach Tailored for Spaces with Ricci Curvature Bounded from Below available in PDF, EPUB and Kindle. The author discusses in which sense general metric measure spaces possess a first order differential structure. Building on this, spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting the author to define Hessian, covariant/exterior derivatives and Ricci curvature.
Lectures on Nonsmooth Differential Geometry
Lectures on Nonsmooth Differential Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Nonsmooth Differential Geometry write by Nicola Gigli. This book was released on 2020-02-10. Lectures on Nonsmooth Differential Geometry available in PDF, EPUB and Kindle. This book provides an introduction to some aspects of the flourishing field of nonsmooth geometric analysis. In particular, a quite detailed account of the first-order structure of general metric measure spaces is presented, and the reader is introduced to the second-order calculus on spaces – known as RCD spaces – satisfying a synthetic lower Ricci curvature bound. Examples of the main topics covered include notions of Sobolev space on abstract metric measure spaces; normed modules, which constitute a convenient technical tool for the introduction of a robust differential structure in the nonsmooth setting; first-order differential operators and the corresponding functional spaces; the theory of heat flow and its regularizing properties, within the general framework of “infinitesimally Hilbertian” metric measure spaces; the RCD condition and its effects on the behavior of heat flow; and second-order calculus on RCD spaces. The book is mainly intended for young researchers seeking a comprehensive and fairly self-contained introduction to this active research field. The only prerequisites are a basic knowledge of functional analysis, measure theory, and Riemannian geometry.
Elliptic PDEs on Compact Ricci Limit Spaces and Applications
Elliptic PDEs on Compact Ricci Limit Spaces and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic PDEs on Compact Ricci Limit Spaces and Applications write by Shouhei Honda. This book was released on 2018-05-29. Elliptic PDEs on Compact Ricci Limit Spaces and Applications available in PDF, EPUB and Kindle. In this paper the author studies elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular the author establishes continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrödinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. The author applies these to the study of second-order differential calculus on such limit spaces.
Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)
Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) write by Boyan Sirakov. This book was released on 2019-02-27. Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) available in PDF, EPUB and Kindle. The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture
A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture write by Francesco Lin. This book was released on 2018-10-03. A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture available in PDF, EPUB and Kindle. In the present work the author generalizes the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a structure which is isomorphic to its conjugate, the author defines the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, the author provides an alternative approach to his disproof of the celebrated Triangulation conjecture.
