000 04690nam a22006135i 4500
001 978-3-7643-8133-2
003 DE-He213
005 20181204132645.0
007 cr nn 008mamaa
008 100301s2007 sz | s |||| 0|eng d
020 _a9783764381332
_9978-3-7643-8133-2
024 7 _a10.1007/978-3-7643-8133-2
_2doi
040 _aISI Library, Kolkata
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
072 7 _aPBMP
_2thema
082 0 4 _a516.36
_223
100 1 _aCapogna, Luca.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 3 _aAn Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem
_h[electronic resource] /
_cby Luca Capogna, Scott D. Pauls, Donatella Danielli ; edited by Jeremy T. Tyson.
264 1 _aBasel :
_bBirkhäuser Basel,
_c2007.
300 _aXVI, 224 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematics,
_x0743-1643 ;
_v259
505 0 _aThe Isoperimetric Problem in Euclidean Space -- The Heisenberg Group and Sub-Riemannian Geometry -- Applications of Heisenberg Geometry -- Horizontal Geometry of Submanifolds -- Sobolev and BV Spaces -- Geometric Measure Theory and Geometric Function Theory -- The Isoperimetric Inequality in ? -- The Isoperimetric Profile of ? -- Best Constants for Other Geometric Inequalities on the Heisenberg Group.
520 _aThe past decade has witnessed a dramatic and widespread expansion of interest and activity in sub-Riemannian (Carnot-Caratheodory) geometry, motivated both internally by its role as a basic model in the modern theory of analysis on metric spaces, and externally through the continuous development of applications (both classical and emerging) in areas such as control theory, robotic path planning, neurobiology and digital image reconstruction. The quintessential example of a sub Riemannian structure is the Heisenberg group, which is a nexus for all of the aforementioned applications as well as a point of contact between CR geometry, Gromov hyperbolic geometry of complex hyperbolic space, subelliptic PDE, jet spaces, and quantum mechanics. This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile. It presents a detailed description of Heisenberg submanifold geometry and geometric measure theory, which provides an opportunity to collect for the first time in one location the various known partial results and methods of attack on Pansu's problem. As such it serves simultaneously as an introduction to the area for graduate students and beginning researchers, and as a research monograph focused on the isoperimetric problem suitable for experts in the area.
650 0 _aGlobal differential geometry.
650 0 _aTopological Groups.
650 0 _aCell aggregation
_xMathematics.
650 0 _aDifferential equations, partial.
650 0 _aGlobal analysis.
650 0 _aSystems theory.
650 1 4 _aDifferential Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21022
650 2 4 _aTopological Groups, Lie Groups.
_0http://scigraph.springernature.com/things/product-market-codes/M11132
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
_0http://scigraph.springernature.com/things/product-market-codes/M28027
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
650 2 4 _aSystems Theory, Control.
_0http://scigraph.springernature.com/things/product-market-codes/M13070
700 1 _aPauls, Scott D.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aDanielli, Donatella.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aTyson, Jeremy T.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783764391850
776 0 8 _iPrinted edition:
_z9783764381325
830 0 _aProgress in Mathematics,
_x0743-1643 ;
_v259
856 4 0 _uhttps://doi.org/10.1007/978-3-7643-8133-2
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c425557
_d425557