Conformal Fractional Dirac Operator and Spinorial Q-curvature

Fuente: arXiv
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Main Author: Maalaoui, Ali
Format: Preprint
Published: 2025
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author Maalaoui, Ali
author_facet Maalaoui, Ali
contents In this paper we introduce the conformal fractional Dirac operator and its associated fractional spinorial Yamabe problem. We also present a Caffarelli-Silvestre type extension for this fractional operator, allowing us to express it as a Dirichlet-to-Neumann type operator. As a consequence, we exhibit energy inequalities associated to this operator along with a weighted type Sobolev inequality for spinors. In the second part of the paper, we focus on the critical operator (which can be local or non-local depending on the evenness of the dimension). We introduce a Q-curvature operator, acting on spinors generalizing the classical notion of the scalar Q-curvature.
format Preprint
id arxiv_https___arxiv_org_abs_2505_05706
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Conformal Fractional Dirac Operator and Spinorial Q-curvature
Maalaoui, Ali
Differential Geometry
Analysis of PDEs
53C27, 30F45
In this paper we introduce the conformal fractional Dirac operator and its associated fractional spinorial Yamabe problem. We also present a Caffarelli-Silvestre type extension for this fractional operator, allowing us to express it as a Dirichlet-to-Neumann type operator. As a consequence, we exhibit energy inequalities associated to this operator along with a weighted type Sobolev inequality for spinors. In the second part of the paper, we focus on the critical operator (which can be local or non-local depending on the evenness of the dimension). We introduce a Q-curvature operator, acting on spinors generalizing the classical notion of the scalar Q-curvature.
title Conformal Fractional Dirac Operator and Spinorial Q-curvature
topic Differential Geometry
Analysis of PDEs
53C27, 30F45
url https://arxiv.org/abs/2505.05706