03461nmm a2200433 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001800139245018100157250001700338260004100355300003200396505040800428653002600836653003600862653004600898653001900944653003300963653003500996653003501031653002301066653002801089653005501117653002001172653003501192700003401227700003001261700002801291710003401319041001901353989003601372490002801408856007201436082001101508520150801519EB000392385EBX0100000000000000024543800000000000000.0cr|||||||||||||||||||||130626 ||| eng a97837643813321 aCapogna, Luca00aAn Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric ProblemhElektronische Ressourcecby Luca Capogna, Donatella Danielli, Scott D. Pauls, Jeremy Tyson a1st ed. 2007 aBaselbBirkhĂ¤user Baselc2007, 2007 aXVI, 224 pbonline resource0 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 aDifferential Geometry aDifferential equations, partial aGlobal Analysis and Analysis on Manifolds aSystems theory aGlobal differential geometry aCell aggregation / Mathematics aPartial Differential Equations aTopological Groups aSystems Theory, Control aManifolds and Cell Complexes (incl. Diff.Topology) aGlobal analysis aTopological Groups, Lie Groups1 aDanielli, Donatellae[author]1 aPauls, Scott D.e[author]1 aTyson, Jeremye[author]2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aProgress in Mathematics uhttps://doi.org/10.1007/978-3-7643-8133-2?nosfx=yxVerlag3Volltext0 a516.36 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