A holographic principle for the existence of parallel spinor fields and an inequality of Shi-Tam type

Autor: Hijazi, Oussama, Montiel, Sebastián

Publikováno v: Asian Journal of Mathematics, International Press, 2014, 18, pp.489 - 506

Suppose that $\Sigma=\partial M$ is the $n$-dimensional boundary of a connected compact Riemannian spin manifold $( M,\langle\;,\;\rangle)$ with non-negative scalar curvature, and that the (inward) mean curvature $H$ of $\Sigma$ is positive. We show

Externí odkaz: http://arxiv.org/abs/1502.04859

A holographic principle for the existence of imaginary Killing spinors

Autor: Sebastián Montiel, Oussama Hijazi, Simon Raulot

Publikováno v: Journal of Geometry and Physics
Journal of Geometry and Physics, Elsevier, 2015, 91, pp.12-28. ⟨10.1016/j.geomphys.2015.01.012⟩

Suppose that $\Sigma=\partial\Omega$ is the $n$-dimensional boundary, with positive (inward) mean curvature $H$, of a connected compact $(n+1)$-dimensional Riemannian spin manifold $(\Omega^{n+1},g)$ whose scalar curvature $R\ge -n(n+1)k^2$, for some

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0b208f52946848660579cd5e8c8f6be7
https://hal.archives-ouvertes.fr/hal-01116656

On a Liu--Yau type inequality for surfaces

Autor: Oussama Hijazi, Sebastián Montiel, Simon Raulot

Publikováno v: Pacific Journal of Mathematics
Pacific Journal of Mathematics, 2014, 272 (1), pp.177-199. ⟨10.2140/pjm.2014.272.177⟩

International audience; Let $\Omega$ be a compact and mean-convex domain with smooth boundary $\Sigma:=\partial\Omega$, in an initial data set $(M^3,g,K)$, which has no apparent horizon in its interior. If $\Sigma$ is spacelike in a spacetime $(\E^4,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::48d2ffc0a01701c70a8bfd672a7ad1fb

Uniqueness of the AdS spacetime among static vacua with prescribed null infinity

Autor: Sebastián Montiel, Oussama Hijazi

Publikováno v: Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics, International Press, 2014, 18 (1), pp.177-203. ⟨10.4310/ATMP.2014.v18.n1.a4⟩
Adv. Theor. Math. Phys. 18, no. 1 (2014), 177-203

International audience; We prove that an (n+1)-dimensional spin static vacuum with negative cosmological constant whose null infinity has a boundary admitting a non-trivial Killing spinor field is the AdS spacetime. As a consequence, we generalize pr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::48dbc876d07068fac715319b4d856d76
https://hal.archives-ouvertes.fr/hal-01097023/file/Hijazi-Montiel-ATMP.pdf

Rigidité conforme des hémisphères S^4_+ et S^6_+

Autor: Raulot, Simon

Publikováno v: Mathematische Zeitschrift
Mathematische Zeitschrift, Springer, 2012, 271 (3-4), pp.707-714. ⟨10.1007/s00209-011-0885-8⟩

Let (M,g) be a four or six dimensional compact Riemannian manifold which is locally conformally flat and assume that its boundary is totally umbilical. In this note, we prove that if the Euler characteristic of M is equal to 1 and if its Yamabe invar

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=arXiv_dedup_::76cf8799d3b83021699a82cc4532ac44
https://hal.archives-ouvertes.fr/hal-00585754