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The Resource The metric induced by the Robin function

The metric induced by the Robin function

Label
The metric induced by the Robin function
Title
The metric induced by the Robin function
Creator
Contributor
Author
Subject
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
Instantiates
Publication
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 half-space
  • Sufficient conditions for completeness of the [capital Greek]Lambda-metric
  • 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
  • Levi-curvature
  • 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
Publication
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 half-space
  • Sufficient conditions for completeness of the [capital Greek]Lambda-metric
  • 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
  • Levi-curvature
  • 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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