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 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
- 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 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
- 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/The-metric-induced-by-the-Robin-function/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/The-metric-induced-by-the-Robin-function/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>
