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- GJMS_operator 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 Graham, Jenne, Mason & Sparling (1992).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 integerThe 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.".
- GJMS_operator wikiPageID "25525269".
- GJMS_operator wikiPageRevisionID "597640222".
- GJMS_operator hasPhotoCollection GJMS_operator.
- GJMS_operator subject Category:Conformal_geometry.
- GJMS_operator subject Category:Differential_operators.
- GJMS_operator type Abstraction100002137.
- GJMS_operator type DifferentialOperators.
- GJMS_operator type Function113783816.
- GJMS_operator type MathematicalRelation113783581.
- GJMS_operator type Operator113786413.
- GJMS_operator type Relation100031921.
- GJMS_operator 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.".
- GJMS_operator label "GJMS operator".
- GJMS_operator sameAs m.09rsd2b.
- GJMS_operator sameAs Q5513562.
- GJMS_operator sameAs Q5513562.
- GJMS_operator sameAs GJMS_operator.
- GJMS_operator wasDerivedFrom GJMS_operator?oldid=597640222.
- GJMS_operator isPrimaryTopicOf GJMS_operator.