By Dmitri Burago, Yuri Burago, Sergei Ivanov
"Metric geometry" is an method of geometry in keeping with the proposal of size on a topological area. This method skilled a truly speedy improvement within the previous few a long time and penetrated into many different mathematical disciplines, reminiscent of staff idea, dynamical structures, and partial differential equations. the target of this graduate textbook is twofold: to offer a close exposition of uncomplicated notions and strategies utilized in the idea of size areas, and, extra in general, to supply an ordinary advent right into a extensive number of geometrical themes regarding the concept of distance, together with Riemannian and Carnot-Caratheodory metrics, the hyperbolic aircraft, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic areas, convergence of metric areas, and Alexandrov areas (non-positively and non-negatively curved spaces). The authors are inclined to paintings with "easy-to-touch" mathematical gadgets utilizing "easy-to-visualize" equipment. The authors set a demanding aim of constructing the center components of the publication available to first-year graduate scholars. so much new suggestions and techniques are brought and illustrated utilizing easiest situations and fending off technicalities. The ebook includes many workouts, which shape an integral part of exposition.
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Additional resources for A Course in Metric Geometry (Graduate Studies in Mathematics, Volume 33)
Math. Phys. 8, 159–170 (1975) 29. : Probability measures on metric spaces of nonpositive curvature. In: Auscher P. et al. ) Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces (Contemp. Math. vol. 338, Amer. Math. Soc. 2003) 30. : An elementary proof of arithmetic-geometric mean inequality of the weighted Riemannian mean of positive definite matrices, to appear in Linear Algebra Appl. 31. 1 Introduction The Kalman-Bucy filter  (KF) is a very popular method in engineering, that allows to compute an estimate of the state of a dynamical system from several sensors measurements, possibly corrupted by measurement’s noise.
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Means of positive linear operators. Math. Ann. 246, 205–224 (1980) 20. : The geometric mean, matrices, metrics and more. Am. Math. Mon. 108, 797–812 (2001) 21. : Monotonic properties of the least squares mean. Math. Ann. 351, 267–279 (2011) 22. : The matrix power means and the Karcher mean. J. Funct. Anal. 262, 1498–1514 (2012) 23. : Means and averaging in the group of rotations. SIAM J. Matrix Anal. Appl. 24, 1–16 (2002) 24. : A differential geometric approach to the geometric mean of symmetric positive definite matrices.