Intrinsic regular hypersurfaces and PDEs - Bigolin, Francesco
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A fundamental problem of geometric analysis is the investigation of the interplay between a given hypersurface and its normal. Typically, this investigation consists in the study of suitable PDEs once a coordinates' system for the hypersurface has been fixed. In the spirit of this strategy, this book studies the relationships between weak solutions of nonlinear first order PDEs and intrinsic regular hypersurfaces in the setting of the Heisenberg group, endowed with a not euclidean metric called Carnot-Caratheodory metric. Intrinsic regular hypersurfaces are topological codimension 1 surfaces…mehr

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Produktbeschreibung
A fundamental problem of geometric analysis is the investigation of the interplay between a given hypersurface and its normal. Typically, this investigation consists in the study of suitable PDEs once a coordinates' system for the hypersurface has been fixed. In the spirit of this strategy, this book studies the relationships between weak solutions of nonlinear first order PDEs and intrinsic regular hypersurfaces in the setting of the Heisenberg group, endowed with a not euclidean metric called Carnot-Caratheodory metric. Intrinsic regular hypersurfaces are topological codimension 1 surfaces which are regular by the intrinsic point of view of the group and its differential structure. In particular the problem of the regularity of the parametrization of a hypersurface is investigated through well-known results of the theory of weak solutions of conservation laws, a special class of non linear first order PDEs with which the normal of the hypersurface can be described. This book isrecommended to people interested in geometry and analysis in metric spaces.
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Autorenporträt
born in 1981, Ph.D. in Mathematics in 2009 at the University of Trento, Italy; now teaching Mathematical Analysis in the universities of Bolzano and Trento. Scientific interests in analysis in metric spaces, Heisenberg Group, conservation laws and non linear PDEs.