Geometric Analysis of the Bergman Kernel and Metric (Graduate Texts in Mathematics)

Geometric Analysis of the Bergman Kernel and Metric (Graduate Texts in Mathematics)

Steven G Krantz

Language: English

Pages: 292

ISBN: 1461479231

Format: PDF / Kindle (mobi) / ePub


This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection of exercises which will be of interest to both graduate students and experienced mathematicians.

Graduate students who have taken courses in complex variables
and have a basic background in real and functional analysis will find this textbook appealing. Applicable courses for either main or supplementary usage include those in complex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complex analysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the many exciting aspects of Bergman's theory.

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Complex Monge–Ampère, and uniformly elliptic, equations, Comm. Pure Appl. Math. 38(1985), 209–252. [CAR] L. Carleson, Selected Problems on Exceptional Sets, Van Nostrand, Princeton, NJ, 1967. [CCP] G. Carrier, M. Crook, and C. Pearson, Functions of a Complex Variable, McGraw-Hill, New York, 1966. [CAT1] D. Catlin, Necessary conditions for subellipticity of the Neumann problem, Ann. Math. 117(1983), 147–172.MathSciNet [CAT2] D. Catlin, Subelliptic estimates for the Neumann problem, Ann.

strongly pseudoconvex domains in with smooth boundary, Trans. Am. Math. Soc. 207(1975), 219–240. [GRL] H. Grauert and I. Lieb, Das Ramirezsche Integral und die Gleichung im Bereich der beschränkten Formen, Rice University Studies 56(1970), 29–50.MathSciNet [GKK] R. E. Greene, K.-T. Kim, and S. G. Krantz, The Geometry of Complex Domains, Birkhäuser Publishing, Boston, MA, 2011. [GRK1] R. E. Greene and S. G. Krantz, Stability properties of the Bergman kernel and curvature properties of

spaces, smoothness of functions, and approximation theory, Expositiones Math. 3(1983), 193–260.MathSciNet [KRA13] S. G. Krantz, Characterizations of smooth domains in by their biholomorphic self maps, Am. Math. Monthly 90(1983), 555–557.MathSciNet [KRA14] S. G. Krantz, A Guide to Functional Analysis, Mathematical Association of America, Washington, D.C., 2013, to appear. [KRA15] S. G. Krantz, A direct connection between the Bergman and Szegő projections, Complex Analysis and Operator

the conjugation map Φ from the conjugation map provided by Ebin’s theorem. That completes the argument. □  Since we introduced the C k metric for the space of automorphisms, it is worthwhile to formulate a result for that topology. We have: Theorem 5.4.2. Let Ω be a smoothly bounded, finite-type domain in . Equip with the C k topology, some integer k ≥ 0. Assume that Ω has compact automorphism group in the C k topology. Then there is an ε > 0 so that if Ω′ is a smoothly bounded, finite-type

[KRA4] for details of this important topic. Here we only briefly review the key concepts. In studying the operator, it is convenient to treat the second order, self-adjoint operator given by It is shown that this partial differential operator has a right inverse N, which is known as the -Neumann operator. Let be a fixed domain on which the equation is always solvable when α is a closed (0, 1) form (i.e., a domain of holomorphy—in other words, a pseudoconvex domain). Let be the Bergman

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