{"product_id":"comparison-finsler-geometry-9783030806521","title":"Comparison Finsler Geometry","description":"\u003cp\u003eThis monograph presents recent developments in comparison geometry and geometric analysis on Finsler manifolds. Generalizing the weighted Ricci curvature into the Finsler setting, the author systematically derives the fundamental geometric and analytic inequalities in the Finsler context. Relying only upon knowledge of differentiable manifolds, this treatment offers an accessible entry point to Finsler geometry for readers new to the area.\u003c\/p\u003e \u003cp\u003eDivided into three parts, the book begins by establishing the fundamentals of Finsler geometry, including Jacobi fields and curvature tensors, variation formulas for arc length, and some classical comparison theorems. Part II goes on to introduce the weighted Ricci curvature, nonlinear Laplacian, and nonlinear heat flow on Finsler manifolds. These tools allow the derivation of the Bochner-Weitzenböck formula and the corresponding Bochner inequality, gradient estimates, Bakry-Ledoux's Gaussian isoperimetric inequality, and functional inequalities in the Finsler setting. Part III comprises advanced topics: a generalization of the classical Cheeger-Gromoll splitting theorem, the curvature-dimension condition, and the needle decomposition. Throughout, geometric descriptions illuminate the intuition behind the results, while exercises provide opportunities for active engagement.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eComparison Finsler Geometry\u003c\/i\u003e offers an ideal gateway to the study of Finsler manifolds for graduate students and researchers. Knowledge of differentiable manifold theory is assumed, along with the fundamentals of functional analysis. Familiarity with Riemannian geometry is not required, though readers with a background in the area will find their insights are readily transferrable.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=AUTH-14630258\"\u003eShin-Ichi Ohta\u003c\/a\u003e\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 10\/10\/2022\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 316\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.05lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.71d\u003cbr\u003e\u003cb\u003eISBN13:\u003c\/b\u003e 9783030806521\u003cbr\u003e\u003cb\u003eISBN10:\u003c\/b\u003e 3030806529\u003cbr\u003e\u003cb\u003eBISAC Categories:\u003c\/b\u003e\u003cbr\u003e- \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=CAT-MAT\"\u003eMathematics\u003c\/a\u003e | \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=BISAC-MAT012030\"\u003eGeometry | Differential\u003c\/a\u003e\u003cbr\u003e- \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=CAT-MAT\"\u003eMathematics\u003c\/a\u003e | \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=BISAC-MAT034000\"\u003eMathematical Analysis\u003c\/a\u003e\u003cbr\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eAbout the Author\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eShin-ichi Ohta\u003c\/b\u003e is Distinguished Professor of Mathematics at Osaka University, Japan. His research interests lie in comparison geometry and its applications. He is a leading expert in the geometry and analysis of weighted Ricci curvature.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":44692132266221,"sku":"9783030806521","price":239.98,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0550\/8097\/6621\/products\/img_90bfa2bb-8ee7-48d9-9efa-6911eea2fb1a.jpg?v=1703737400","url":"https:\/\/sureshotbooks.com\/es\/products\/comparison-finsler-geometry-9783030806521","provider":"SureShot Books Publishing LLC","version":"1.0","type":"link"}