About: GJMS operator

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In the mathematical field of differential geometry, the GJMS operators are a family of differential operators, that are defined on a Riemannian manifold. In an appropriate sense, they depend only on the conformal structure of the manifold. The GJMS operators generalize the Paneitz operator and the conformal Laplacian. The initials GJMS are for its discoverers . Properly, the GJMS operator on a conformal manifold of dimension n is a conformally invariant operator between the line bundle of conformal densities of weight k − n/2 for k a positive integer

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rdf:type	yago:Abstraction100002137 yago:Function113783816 yago:MathematicalRelation113783581 yago:Operator113786413 yago:Relation100031921 yago:WikicatDifferentialOperators
rdfs:label	GJMS operator (en)
rdfs:comment	In the mathematical field of differential geometry, the GJMS operators are a family of differential operators, that are defined on a Riemannian manifold. In an appropriate sense, they depend only on the conformal structure of the manifold. The GJMS operators generalize the Paneitz operator and the conformal Laplacian. The initials GJMS are for its discoverers . Properly, the GJMS operator on a conformal manifold of dimension n is a conformally invariant operator between the line bundle of conformal densities of weight k − n/2 for k a positive integer (en)
dct:subject	Conformal geometry Differential operators
Wikipage page ID	25525269 (xsd:integer)
Wikipage revision ID	984945249 (xsd:integer)
Link from a Wikipage to another Wikipage	Volume form Mathematics Density on a manifold Laplace operators in differential geometry Line bundle Ambient construction Conformal geometry Cauchy problem Differential operator Riemannian manifold Differential operators Paneitz operator Charles Fefferman Laplace operator Differential geometry C. Robin Graham Symbol of a differential operator Conformal structure Conformally invariant Null cone
sameAs	GJMS operator GJMS operator GJMS operator GJMS operator
dbp:wikiPageUsesTemplate	dbt:Citation
has abstract	In the mathematical field of differential geometry, the GJMS operators are a family of differential operators, that are defined on a Riemannian manifold. In an appropriate sense, they depend only on the conformal structure of the manifold. The GJMS operators generalize the Paneitz operator and the conformal Laplacian. The initials GJMS are for its discoverers . Properly, the GJMS operator on a conformal manifold of dimension n is a conformally invariant operator between the line bundle of conformal densities of weight k − n/2 for k a positive integer The operators have leading symbol given by a power of the Laplace–Beltrami operator, and have lower order correction terms that ensure conformal invariance. The original construction of the GJMS operators used the ambient construction of Charles Fefferman and Robin Graham. A conformal density defines, in a natural way, a function on the null cone in the ambient space. The GJMS operator is defined by taking density ƒ of the appropriate weight k − n/2 and extending it arbitrarily to a function F off the null cone so that it still retains the same homogeneity. The function ΔkF, where Δ is the ambient Laplace–Beltrami operator, is then homogeneous of degree −k − n/2, and its restriction to the null cone does not depend on how the original function ƒ was extended to begin with, and so is independent of choices. The GJMS operator also represents the obstruction term to a formal asymptotic solution of the Cauchy problem for extending a weight k − n/2 function off the null cone in the ambient space to a harmonic function in the full ambient space. The most important GJMS operators are the critical GJMS operators. In even dimension n, these are the operators Ln/2 that take a true function on the manifold and produce a multiple of the volume form. (en)
prov:wasDerivedFrom	wikipedia-en:GJMS_operator?oldid=984945249&ns=0
page length (characters) of wiki page	2894 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:GJMS_operator
is Link from a Wikipage to another Wikipage of	Ambient construction Paneitz operator C. Robin Graham
is foaf:primaryTopic of	wikipedia-en:GJMS_operator

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