Generalized Willmore energies, Q-curvatures, extrinsic Paneitz operators, and extrinsic Laplacian powers

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00135673" target="_blank" >RIV/00216224:14310/24:00135673 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.worldscientific.com/doi/10.1142/S0219199723500141" target="_blank" >https://www.worldscientific.com/doi/10.1142/S0219199723500141</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0219199723500141" target="_blank" >10.1142/S0219199723500141</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Generalized Willmore energies, Q-curvatures, extrinsic Paneitz operators, and extrinsic Laplacian powers

Popis výsledku v původním jazyce

Over forty years ago, Paneitz, and independently Fradkin and Tseytlin, discovered a fourth-order conformally invariant differential operator, intrinsically defined on a conformal manifold, mapping scalars to scalars. This operator is a special case of the so-termed extrinsic Paneitz operator defined in the case when the conformal manifold is itself a conformally embedded hypersurface. In particular, this encodes the obstruction to smoothly solving the five-dimensional scalar Laplace equation, and suitable higher dimensional analogs, on conformally compact structures with constant scalar curvature. Moreover, the extrinsic Paneitz operator can act on tensors of general type by dint of being defined on tractor bundles. Motivated by a host of applications, we explicitly compute the extrinsic Paneitz operator. We apply this formula to obtain: an extrinsically-coupled Q-curvature for embedded four-manifolds, the anomaly in renormalized volumes for conformally compact five-manifolds with negative constant scalar curvature, Willmore energies for embedded four-manifolds, the local obstruction to smoothly solving the five-dimensional singular Yamabe problem, and new extrinsically-coupled fourth- and sixth-order operators for embedded surfaces and four-manifolds, respectively.

Název v anglickém jazyce

Generalized Willmore energies, Q-curvatures, extrinsic Paneitz operators, and extrinsic Laplacian powers

Popis výsledku anglicky

Over forty years ago, Paneitz, and independently Fradkin and Tseytlin, discovered a fourth-order conformally invariant differential operator, intrinsically defined on a conformal manifold, mapping scalars to scalars. This operator is a special case of the so-termed extrinsic Paneitz operator defined in the case when the conformal manifold is itself a conformally embedded hypersurface. In particular, this encodes the obstruction to smoothly solving the five-dimensional scalar Laplace equation, and suitable higher dimensional analogs, on conformally compact structures with constant scalar curvature. Moreover, the extrinsic Paneitz operator can act on tensors of general type by dint of being defined on tractor bundles. Motivated by a host of applications, we explicitly compute the extrinsic Paneitz operator. We apply this formula to obtain: an extrinsically-coupled Q-curvature for embedded four-manifolds, the anomaly in renormalized volumes for conformally compact five-manifolds with negative constant scalar curvature, Willmore energies for embedded four-manifolds, the local obstruction to smoothly solving the five-dimensional singular Yamabe problem, and new extrinsically-coupled fourth- and sixth-order operators for embedded surfaces and four-manifolds, respectively.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Communications in Contemporary Mathematics

ISSN

0219-1997

e-ISSN

1793-6683

Svazek periodika

26

Číslo periodika v rámci svazku

05

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

50

Strana od-do

1-50

Kód UT WoS článku

001157533200001

EID výsledku v databázi Scopus

2-s2.0-85170275966