The Resource The metric induced by the Robin function
The metric induced by the Robin function
Resource Information
The item The metric induced by the Robin function represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item The metric induced by the Robin function represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 This paper continues Yamaguchi's earlier work on the Robin function for bounded domains in [bold]C[italic superscript]n. Yamaguchi showed that if the domain [italic]D is smoothly bounded and pseudoconvex, then the Robin function and its logarithm are both real analytic strongly pseudoconvex exhaustions of the domain. It follows that they may be used as potentials to define Kähler metrics on the domain. In this paper, the authors study the properties of these Kähler metrics, concentrating on the question of completeness. By using an affine scaling technique to blow up the domain at points near the boundary (the scaling constant grows roughly as the inverse of the distance to the boundary), the authors study in some detail the behaviour of the Robin function and the induced metric near the boundary of the domain. They show that if the domain is either strongly pseudoconvex or geometrically convex, then the metric associated to the logarithm of the Robin function is complete. They also conjecture that this is true in general for any smoothly bounded pseudoconvex domain
 Language
 eng
 Extent
 viii, 156 pages
 Contents

 Metric induced by Robin function
 Strictly pseudoconvex boundary points
 Explicit formulas for a halfspace
 Sufficient conditions for completeness of the [capital Greek]Lambdametric
 An example with [script lowercase]l2([lowercase Greek]Xi, [italic]a) [not greater than or equal to] [italic]c [conditional event/restriction/such that] [script lowercase]l1([lowercase Greek]Xi, [italic]a)[conditional event/restriction/such that]2
 Levicurvature
 Smooth variation of domains
 Boundary behavior of the Robin function [capital Greek]Lambda([lowercase Greek]Xi)
 Proof of Lemma 3.1
 Proof of Lemma 3.1, continued
 Limiting formulas
 Strict plurisubharmonicity of {u2212}[capital Greek]Lambda([lowercase Greek]Xi), log({u2212}[capital Greek]Lambda([lowercase Greek]Xi))
 The Robin function and the Bergman kernel
 Isbn
 9780821825204
 Label
 The metric induced by the Robin function
 Title
 The metric induced by the Robin function
 Language
 eng
 Summary
 This paper continues Yamaguchi's earlier work on the Robin function for bounded domains in [bold]C[italic superscript]n. Yamaguchi showed that if the domain [italic]D is smoothly bounded and pseudoconvex, then the Robin function and its logarithm are both real analytic strongly pseudoconvex exhaustions of the domain. It follows that they may be used as potentials to define Kähler metrics on the domain. In this paper, the authors study the properties of these Kähler metrics, concentrating on the question of completeness. By using an affine scaling technique to blow up the domain at points near the boundary (the scaling constant grows roughly as the inverse of the distance to the boundary), the authors study in some detail the behaviour of the Robin function and the induced metric near the boundary of the domain. They show that if the domain is either strongly pseudoconvex or geometrically convex, then the metric associated to the logarithm of the Robin function is complete. They also conjecture that this is true in general for any smoothly bounded pseudoconvex domain
 Cataloging source
 UkLiU
 http://library.link/vocab/creatorName
 Levenberg, Norman
 http://library.link/vocab/relatedWorkOrContributorDate
 1942
 http://library.link/vocab/relatedWorkOrContributorName
 Yamaguchi, Hiroshi
 Series statement
 Memoirs of the American Mathematical Society
 Series volume
 448
 http://library.link/vocab/subjectName

 Plurisubharmonic functions
 Pseudoconvex domains
 Label
 The metric induced by the Robin function
 Bibliography note
 Includes bibliographical references (page 156)
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Metric induced by Robin function
 Strictly pseudoconvex boundary points
 Explicit formulas for a halfspace
 Sufficient conditions for completeness of the [capital Greek]Lambdametric
 An example with [script lowercase]l2([lowercase Greek]Xi, [italic]a) [not greater than or equal to] [italic]c [conditional event/restriction/such that] [script lowercase]l1([lowercase Greek]Xi, [italic]a)[conditional event/restriction/such that]2
 Levicurvature
 Smooth variation of domains
 Boundary behavior of the Robin function [capital Greek]Lambda([lowercase Greek]Xi)
 Proof of Lemma 3.1
 Proof of Lemma 3.1, continued
 Limiting formulas
 Strict plurisubharmonicity of {u2212}[capital Greek]Lambda([lowercase Greek]Xi), log({u2212}[capital Greek]Lambda([lowercase Greek]Xi))
 The Robin function and the Bergman kernel
 Dimensions
 26 cm.
 Extent
 viii, 156 pages
 Isbn
 9780821825204
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Label
 The metric induced by the Robin function
 Bibliography note
 Includes bibliographical references (page 156)
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Metric induced by Robin function
 Strictly pseudoconvex boundary points
 Explicit formulas for a halfspace
 Sufficient conditions for completeness of the [capital Greek]Lambdametric
 An example with [script lowercase]l2([lowercase Greek]Xi, [italic]a) [not greater than or equal to] [italic]c [conditional event/restriction/such that] [script lowercase]l1([lowercase Greek]Xi, [italic]a)[conditional event/restriction/such that]2
 Levicurvature
 Smooth variation of domains
 Boundary behavior of the Robin function [capital Greek]Lambda([lowercase Greek]Xi)
 Proof of Lemma 3.1
 Proof of Lemma 3.1, continued
 Limiting formulas
 Strict plurisubharmonicity of {u2212}[capital Greek]Lambda([lowercase Greek]Xi), log({u2212}[capital Greek]Lambda([lowercase Greek]Xi))
 The Robin function and the Bergman kernel
 Dimensions
 26 cm.
 Extent
 viii, 156 pages
 Isbn
 9780821825204
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/ThemetricinducedbytheRobinfunction/raPeiGiqdXw/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/ThemetricinducedbytheRobinfunction/raPeiGiqdXw/">The metric induced by the Robin function</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>