Conformal Fractional Dirac Operator and Spinorial Q-curvature
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912367296643072 |
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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 |