This article is available for purchase or by subscription. See below.
Abstract
|
In this paper, we introduce new aspects in conformal geometry of some very natural
second-order differential operators. These operators are termed shift operators. In
the flat space, they are intertwining operators which are closely related to
symmetry breaking differential operators. In the curved case, they are closely
connected with ideas of holography and the works of Fefferman–Graham,
Gover–Waldron and one of the authors. In particular, we obtain an alternative
description of the so-called residue families in conformal geometry in terms of
compositions of shift operators. This relation allows easy new proofs of some of
their basic properties. In addition, we derive new holographic formulas for
-curvatures
in even dimension. Since these turn out to be equivalent to earlier holographic
formulas, the novelty here is their conceptually very natural proof. The overall
discussion leads to a unification of constructions in representation theory and
conformal geometry.
|
PDF Access Denied
We have not been able to recognize your IP address
18.221.53.209
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
Poincaré metrics, ambient metrics, conformal geometry,
symmetry breaking operators, residue families, shift
operators, GJMS operators, $Q$-curvature
|
Mathematical Subject Classification 2010
Primary: 35J30, 53A30, 53B20
Secondary: 35Q76, 53C25, 58J50
|
Milestones
Received: 20 August 2018
Accepted: 20 December 2019
Published: 3 December 2020
|
|