Geometric Analysis on Real Analytic Manifolds
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Beschreibung
This monograph provides some useful tools for performing global geometric analysis on real analytic manifolds. At the core of the methodology of the book is a variety of descriptions for the topologies for the space of real analytic sections of a real analytic vector bundle and for the space of real analytic mappings between real analytic manifolds. Among the various descriptions for these topologies is a development of geometric seminorms for the space of real analytic sections. To illustrate the techniques in the book, a number of fundamental constructions in differential geometry are shown to induce continuous mappings on spaces of real analytic sections and mappings.
Aimed at researchers at the level of Doctoral students and above, the book introduces the reader to the challenges and opportunities of real analytic analysis and geometry.
This monograph provides some useful tools for performing global geometric analysis on real analytic manifolds. At the core of the methodology of the book is a variety of descriptions for the topologies for the space of real analytic sections of a real analytic vector bundle and for the space of real analytic mappings between real analytic manifolds. Among the various descriptions for these topologies is a development of geometric seminorms for the space of real analytic sections. To illustrate the techniques in the book, a number of fundamental constructions in differential geometry are shown to induce continuous mappings on spaces of real analytic sections and mappings.
Aimed at researchers at the level of Doctoral students and above, the book introduces the reader to the challenges and opportunities of real analytic analysis and geometry.
First comprehensive treatment of real analytic functional analysis with emphasis on differential geometry Includes many separately interesting geometric techniques for geometric analysis on manifolds, for other regularity With full detailed proofs and application of techniques to new results about continuity of geometric operations
Autor*in
Andrew D. Lewis
Themen in »Geometric Analysis on Real Analytic Manifolds«
Functional Analysis Real Analytic Analysis Geometric Analysis Analysis on Manifolds Difefrential Geometry Global Analysis Seminorms for the Real Analytic Topology Global Geometric Analysis on Real Analytic Manifolds Space of Real Analytic Mappings Geometric Seminorms