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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
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function off the null cone in the ambient space to a harmonic function in the full ambient space.
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off the null cone so that it still retains the same homogeneity. The function Δ
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that take a true function on the manifold and produce a multiple of the
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in the ambient space. The GJMS operator is defined by taking density
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Properly, the GJMS operator on a conformal manifold of dimension
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The original construction of the GJMS operators used the
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of the manifold. The GJMS operators generalize the
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143:. The initials GJMS are for its discoverers
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48:introducing citations to additional sources
320:and extending it arbitrarily to a function
403:Journal of the London Mathematical Society
366:The most important GJMS operators are the
145:Graham, Jenne, Mason & Sparling (1992)
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38:Relevant discussion may be found on the
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370:GJMS operators. In even dimension
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332:, is then homogeneous of degree
31:relies largely or entirely on a
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330:Laplace–Beltrami operator
284:Laplace–Beltrami operator
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268:{\displaystyle L_{k}:E\to E.}
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415:10.1112/jlms/s2-46.3.557
282:given by a power of the
127:, that are defined on a
352:for extending a weight
453:Differential operators
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125:differential operators
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158:operator between the
156:conformally invariant
117:differential geometry
291:ambient construction
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44:improve this article
278:The operators have
181:a positive integer
164:conformal densities
141:conformal Laplacian
133:conformal structure
129:Riemannian manifold
448:Conformal geometry
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405:, Second Series,
295:Charles Fefferman
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399:Graham, C. Robin
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33:single source
29:This article
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113:mathematical
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386:volume form
160:line bundle
442:Categories
392:References
166:of weight
100:April 2024
70:newspapers
423:0024-6107
303:null cone
246:−
240:−
231:→
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115:field of
40:talk page
368:critical
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111:In the
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119:, the
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