Titlebook: Comparison Finsler Geometry; Shin-ichi Ohta Book 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer

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OWL

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

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FLIP

熱心助人

情愛

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

情愛

accessory

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.

用不完

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. .).

DAFT

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 ..