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Conformal Dirac–Einstein equations on manifolds with boundary.

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Abstract

In this paper we study Dirac–Einstein equations on manifolds with boundary, restricted to a conformal class with constant boundary volume, under chiral bag boundary conditions for the Dirac operator. We characterize the bubbling phenomenon, also classifying ground state bubbles. Finally, we prove an Aubin-type inequality and a related existence result.

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Acknowledgements

The authors wish to thank the reviewer for careful reading the manuscript and for the accurate remarks.

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via della Garzetta 48, I-25133, Brescia, Italy

    William Borrelli

  2. Department of Mathematics, Clark University, 950 Main Street, Worcester, MA, 01610, USA

    Ali Maalaoui

  3. Dipartimento di Matematica, Università di Bologna, Piazza di Porta S.Donato 5, 40126, Bologna, Italy

    Vittorio Martino

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  1. William Borrelli
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  2. Ali Maalaoui
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  3. Vittorio Martino
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Correspondence to William Borrelli.

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Communicated by Andrea Mondino.

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Borrelli, W., Maalaoui, A. & Martino, V. Conformal Dirac–Einstein equations on manifolds with boundary.. Calc. Var. 62, 18 (2023). https://doi.org/10.1007/s00526-022-02354-w

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