Global Analysis in Mathematical Physics: Geometric and Stochastic Methods

Front Cover
The first edition of this book entitled Analysis on Riemannian Manifolds and Some Problems of Mathematical Physics was published by Voronezh Univer sity Press in 1989. For its English edition, the book has been substantially revised and expanded. In particular, new material has been added to Sections 19 and 20. I am grateful to Viktor L. Ginzburg for his hard work on the transla tion and for writing Appendix F, and to Tomasz Zastawniak for his numerous suggestions. My special thanks go to the referee for his valuable remarks on the theory of stochastic processes. Finally, I would like to acknowledge the support of the AMS fSU Aid Fund and the International Science Foundation (Grant NZBOOO), which made possible my work on some of the new results included in the English edition of the book. Voronezh, Russia Yuri Gliklikh September, 1995 Preface to the Russian Edition The present book is apparently the first in monographic literature in which a common treatment is given to three areas of global analysis previously consid ered quite distant from each other, namely, differential geometry and classical mechanics, stochastic differential geometry and statistical and quantum me chanics, and infinite-dimensional differential geometry of groups of diffeomor phisms and hydrodynamics. The unification of these topics under the cover of one book appears, however, quite natural, since the exposition is based on a geometrically invariant form of the Newton equation and its analogs taken as a fundamental law of motion.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

IV
3
V
5
VI
7
VII
10
IX
12
X
14
XI
17
XII
19
L
106
LI
107
LII
109
LIV
114
LV
115
LVI
125
LVII
131
LVIII
133

XIII
20
XIV
22
XVI
23
XVII
24
XVIII
26
XIX
28
XX
29
XXI
31
XXII
32
XXIII
39
XXIV
40
XXV
42
XXVI
45
XXVII
47
XXVIII
49
XXIX
50
XXX
53
XXXI
54
XXXII
56
XXXIII
57
XXXIV
58
XXXV
59
XXXVI
67
XXXVII
76
XXXIX
78
XL
80
XLI
83
XLII
87
XLIV
92
XLV
95
XLVI
96
XLVII
97
XLVIII
98
XLIX
101
LXI
134
LXII
136
LXIII
137
LXIV
139
LXVI
141
LXVIII
142
LXX
143
LXXI
147
LXXIII
148
LXXIV
151
LXXV
152
LXXVI
156
LXXVII
164
LXXVIII
171
LXXIX
172
LXXX
175
LXXXI
179
LXXXII
180
LXXXIII
181
LXXXIV
183
LXXXV
185
LXXXVI
186
LXXXVIII
188
XCI
189
XCII
190
XCIV
191
XCV
192
XCVI
193
XCVII
197
XCVIII
198
XCIX
203
C
211
Copyright

Other editions - View all

Common terms and phrases

Popular passages

Page x - In conclusion, the author would like to express his deep gratitude to Candidates of Physicomathematical Sciences, AI Kuz'min and LI Dorman for their valuable advice.
Page viii - Newton equation is introduced by means of the covariant derivative with respect to the Levi-Civita connection of the Riemannian metric, giving rise to the kinetic energy on the configuration space.

Bibliographic information