標(biāo)題: Titlebook: Comparison Finsler Geometry; Shin-ichi Ohta Book 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer [打印本頁] 作者: 劉興旺 時(shí)間: 2025-3-21 16:26
書目名稱Comparison Finsler Geometry影響因子(影響力)
作者: OWL 時(shí)間: 2025-3-21 23:26
Book 2021gradient 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. Througho作者: occult 時(shí)間: 2025-3-22 01:06 作者: FLIP 時(shí)間: 2025-3-22 05:48 作者: 熱心助人 時(shí)間: 2025-3-22 09:24 作者: 情愛 時(shí)間: 2025-3-22 16:51
1439-7382 entry point to studying Finsler geometry for those familiar.This 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作者: 情愛 時(shí)間: 2025-3-22 20:23 作者: accessory 時(shí)間: 2025-3-22 21:20
The Fundamentals of Compressed Sensingconcrete examples..One of the most important observations in this chapter is the absence of “canonical measures” in some Randers spaces. Precisely, we will see that some Randers spaces do not admit any measure whose .-curvature vanishes identically.作者: 用不完 時(shí)間: 2025-3-23 05:18
Compressive Sensing for Vision,e Bochner inequality can be regarded as a nonlinear analogue of the Γ.-criterion..Coupled with the nonlinear heat flow discussed in the next chapter, the Bochner inequality has fruitful applications including gradient estimates (Chap. .), isoperimetric inequalities (Chap. .), and functional inequalities (Chap. .).作者: DAFT 時(shí)間: 2025-3-23 06:42
Sparse Representations in Radar,t these three chapters, we assume the compactness of . to avoid delicate technical issues. In this chapter, we show the ..- and ..-. followed by the . and .. We will also see that the ..- and ..-gradient estimates are both equivalent to the lower weighted Ricci curvature bound ..作者: 死亡率 時(shí)間: 2025-3-23 10:23 作者: 堅(jiān)毅 時(shí)間: 2025-3-23 15:06 作者: 許可 時(shí)間: 2025-3-23 19:07
The Bochner–Weitzenb?ck Formulae Bochner inequality can be regarded as a nonlinear analogue of the Γ.-criterion..Coupled with the nonlinear heat flow discussed in the next chapter, the Bochner inequality has fruitful applications including gradient estimates (Chap. .), isoperimetric inequalities (Chap. .), and functional inequalities (Chap. .).作者: 槍支 時(shí)間: 2025-3-23 22:25
Gradient Estimatest these three chapters, we assume the compactness of . to avoid delicate technical issues. In this chapter, we show the ..- and ..-. followed by the . and .. We will also see that the ..- and ..-gradient estimates are both equivalent to the lower weighted Ricci curvature bound ..作者: 1分開 時(shí)間: 2025-3-24 05:46
Curvatureads us to a useful and inspiring description of the Finsler curvature as the Riemannian curvature of ... The metric .. is also called an ., and its application to the Riemannian characterization of the Finsler curvature goes back to Ottó Varga.作者: 抗體 時(shí)間: 2025-3-24 06:57 作者: 額外的事 時(shí)間: 2025-3-24 13:25 作者: 仔細(xì)閱讀 時(shí)間: 2025-3-24 16:38 作者: anarchist 時(shí)間: 2025-3-24 19:55 作者: Lobotomy 時(shí)間: 2025-3-25 00:47 作者: 范例 時(shí)間: 2025-3-25 06:23 作者: indigenous 時(shí)間: 2025-3-25 09:46
Computation of eigenvalues and eigenvectors,This argument goes back to Ludwig Berwald’s important posthumous paper..The appearance of a geodesic variation reminds us of a characterization of covariant derivatives by using the Riemannian metric .. associated with a vector field .? whose integral curves are geodesics. In fact, this viewpoint le作者: AXIS 時(shí)間: 2025-3-25 14:09
https://doi.org/10.1007/BFb0116611 introduce Berwald spaces, Hilbert and Funk geometries, and Teichmüller spaces and discuss their characteristic properties..We will revisit some of these examples in Chap. . in the context of measured Finsler manifolds (i.e., Finsler manifolds equipped with measures).作者: optic-nerve 時(shí)間: 2025-3-25 17:37 作者: 脊椎動(dòng)物 時(shí)間: 2025-3-25 21:17 作者: FIS 時(shí)間: 2025-3-26 00:33 作者: 赤字 時(shí)間: 2025-3-26 07:22 作者: 嘮叨 時(shí)間: 2025-3-26 11:02 作者: maudtin 時(shí)間: 2025-3-26 14:49
Compressive Sensing for Vision,establish the existence and the regularity of global solutions to the heat equation. Coupled with the Bochner inequalities in the previous chapter, the analysis of heat flow leads to various analytic and geometric applications as we will see in the following chapters. We remark that, due to the nonl作者: 喊叫 時(shí)間: 2025-3-26 17:10
Sparse Representations in Radar,we present three kinds of applications of the Bochner inequality by generalizing the Γ-calculus to the Finsler setting (the so-called . Γ.)..Throughout these three chapters, we assume the compactness of . to avoid delicate technical issues. In this chapter, we show the ..- and ..-. followed by the .作者: 可轉(zhuǎn)變 時(shí)間: 2025-3-26 23:18 作者: 節(jié)約 時(shí)間: 2025-3-27 04:16 作者: 無動(dòng)于衷 時(shí)間: 2025-3-27 08:24 作者: fastness 時(shí)間: 2025-3-27 11:09
Properties of Geodesicstion for the energy functional. To this end, some important quantities such as the fundamental and Cartan tensors are introduced. We will see that the metric definition of geodesics coincides with the variational definition as solutions to the geodesic equation. We also prove the Finsler analogue of the Hopf–Rinow theorem.作者: pacific 時(shí)間: 2025-3-27 14:54
Examples of Finsler Manifolds introduce Berwald spaces, Hilbert and Funk geometries, and Teichmüller spaces and discuss their characteristic properties..We will revisit some of these examples in Chap. . in the context of measured Finsler manifolds (i.e., Finsler manifolds equipped with measures).作者: 一小塊 時(shí)間: 2025-3-27 20:44 作者: ANTH 時(shí)間: 2025-3-28 01:12
https://doi.org/10.1007/978-3-030-80650-7Finsler geometry; Finsler manifolds; Introduction to Finsler geometry; Comparison geometry in Finsler c作者: DOLT 時(shí)間: 2025-3-28 05:10 作者: Bridle 時(shí)間: 2025-3-28 09:57
Donald J. Rose,Ralph A. WilloughbyIn this chapter, as a warm-up before the general theory of Finsler manifolds, we consider normed spaces and discuss some characterizations of inner product spaces among normed spaces. These special properties of inner product spaces will help us to understand the difference between Riemannian and Finsler manifolds.作者: 討厭 時(shí)間: 2025-3-28 10:47
Gary H. Glaser,Michael S. SalibaIn this chapter, we begin with Minkowski normed spaces which appear as tangent spaces of Finsler manifolds, and recall Euler’s homogeneous function theorem as an important calculus tool throughout the book. Then we give the definition of a Finsler manifold, followed by some examples and a naturally induced (asymmetric) distance structure.作者: glacial 時(shí)間: 2025-3-28 17:33 作者: 沒有準(zhǔn)備 時(shí)間: 2025-3-28 18:49
Efficient Sparse Representation and ModelingIn this chapter, we consider the natural energy functional (for functions) and the corresponding Sobolev spaces. Then we introduce the . in a way that its associated harmonic functions are minimizers of the energy functional. We also show the . as the first analytic comparison theorem.作者: 使成整體 時(shí)間: 2025-3-29 00:33
https://doi.org/10.1007/978-3-031-01519-9This chapter is devoted to a geometric application of the improved Bochner inequality, the . (also called the .). This is one of the most important geometric applications of the Γ-calculus. The asymptotic behavior of (nonlinear or linearized) heat semigroups for large time will play an essential role. A related analysis also shows the ..作者: 夜晚 時(shí)間: 2025-3-29 04:11 作者: 同音 時(shí)間: 2025-3-29 08:02
Finsler ManifoldsIn this chapter, we begin with Minkowski normed spaces which appear as tangent spaces of Finsler manifolds, and recall Euler’s homogeneous function theorem as an important calculus tool throughout the book. Then we give the definition of a Finsler manifold, followed by some examples and a naturally induced (asymmetric) distance structure.作者: 節(jié)約 時(shí)間: 2025-3-29 14:34
Covariant DerivativesIn this chapter, we revisit the geodesic equation and give an appropriate definition of . of vector fields (associated with the Chern connection). Our argument will be heuristic and is motivated by a Riemannian characterization.作者: 隱藏 時(shí)間: 2025-3-29 16:20
The Nonlinear LaplacianIn this chapter, we consider the natural energy functional (for functions) and the corresponding Sobolev spaces. Then we introduce the . in a way that its associated harmonic functions are minimizers of the energy functional. We also show the . as the first analytic comparison theorem.作者: exclamation 時(shí)間: 2025-3-29 22:18
Bakry–Ledoux Isoperimetric InequalityThis chapter is devoted to a geometric application of the improved Bochner inequality, the . (also called the .). This is one of the most important geometric applications of the Γ-calculus. The asymptotic behavior of (nonlinear or linearized) heat semigroups for large time will play an essential role. A related analysis also shows the ..作者: Harbor 時(shí)間: 2025-3-30 02:32
Comparison Finsler Geometry978-3-030-80650-7Series ISSN 1439-7382 Series E-ISSN 2196-9922 作者: 譏笑 時(shí)間: 2025-3-30 06:52
Sparse Matrices and their Applicationstion for the energy functional. To this end, some important quantities such as the fundamental and Cartan tensors are introduced. We will see that the metric definition of geodesics coincides with the variational definition as solutions to the geodesic equation. We also prove the Finsler analogue of the Hopf–Rinow theorem.作者: Myocarditis 時(shí)間: 2025-3-30 08:21
https://doi.org/10.1007/BFb0116611 introduce Berwald spaces, Hilbert and Funk geometries, and Teichmüller spaces and discuss their characteristic properties..We will revisit some of these examples in Chap. . in the context of measured Finsler manifolds (i.e., Finsler manifolds equipped with measures).作者: 訓(xùn)誡 時(shí)間: 2025-3-30 12:48 作者: dendrites 時(shí)間: 2025-3-30 16:58
Properties of Geodesicstion for the energy functional. To this end, some important quantities such as the fundamental and Cartan tensors are introduced. We will see that the metric definition of geodesics coincides with the variational definition as solutions to the geodesic equation. We also prove the Finsler analogue of作者: Fsh238 時(shí)間: 2025-3-30 21:59
CurvatureThis argument goes back to Ludwig Berwald’s important posthumous paper..The appearance of a geodesic variation reminds us of a characterization of covariant derivatives by using the Riemannian metric .. associated with a vector field .? whose integral curves are geodesics. In fact, this viewpoint le作者: 厭惡 時(shí)間: 2025-3-31 04:02 作者: 愛國者 時(shí)間: 2025-3-31 06:06
Variation Formulas for Arclength along geodesics, including the study of cut and conjugate points. The first variation formula is closely related to the geodesic equation, which was introduced as the Euler–Lagrange equation for the energy functional. The second variation formula will be related to the flag curvature.作者: 名字的誤用 時(shí)間: 2025-3-31 12:52 作者: 推崇 時(shí)間: 2025-3-31 14:18
