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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Geometric Inequalities (Paperback, Softcover reprint of the original 1st ed. 1988)
Loot Price: R4,365
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Geometric Inequalities (Paperback, Softcover reprint of the original 1st ed. 1988)
Series: Grundlehren der mathematischen Wissenschaften, 285
Expected to ship within 10 - 15 working days
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Geometrie inequalities have a wide range of applieations-within
geometry itself as weIl as beyond its limits. The theory of
funetions of a eomplex variable, the ealculus of variations in the
large, embedding theorems of funetion spaees, a priori estimates
for solutions of differential equations yield many sueh examples.
We have attempted to piek out the most general inequalities and, in
model eases, we exhibit effeetive geometrie eonstruetions and the
means of proving sueh inequalities. A substantial part of this book
deals with isoperimetrie inequalities and their generalizations,
but, for all their variety, they do not exhaust the eontents ofthe
book. The objeets under eonsideration, as a rule, are quite
general. They are eurves, surfaees and other manifolds, embedded in
an underlying space or supplied with an intrinsie metrie. Geometrie
inequalities, used for different purposes, appear in different
eontexts-surrounded by a variety ofteehnieal maehinery, with
diverse require- ments for the objeets under study. Therefore the
methods of proof will differ not only from ehapter to ehapter, but
even within individual seetions. An inspeetion of monographs on
algebraie and funetional inequalities ([HLP], [BeB], [MV], [MM])
shows that this is typical for books of this type.
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