Dirac Operators on Time Flat Submanifolds with Applications

An Alexandrov theorem in Minkowski spacetime

“…Conversely, it is important to remark that, provided that Σ spans a compact spacelike domain Ω of E, any choice of f ∈ C ∞ (Σ) determines a factorization through another spacelike hypersurface which can be obtained from Ω through a suitable deformation. We refer to [HMR2] for a proof of this result.…”

“…Remark 1. It should be point out that in [HMR2] we investigate the rigidity of time flat submanifolds in Minkowski spacetime using a similar method. However the Dirac-type operator we used in this paper is not the one study in the present work.…”

An Alexandrov theorem in Minkowski spacetime

“…Conversely, it is important to observe that, provided that Σ spans a compact spacelike domain Ω of E, any choice of f ∈ C ∞ (Σ) determines a factorization through another spacelike hypersurface which can be obtained from Ω through a suitable deformation. We refer to [HMR2] for a proof of this result.…”

“…The proof of this result relies on a conformal eigenvalue estimate for a Dirac-type operator acting on spinors of Σ (see [HM,HMR1,HMR2]) and especially on a careful treatment of its equality case.…”

“…Remark 1. It should be pointed out that in [HMR2] we investigate the rigidity of time flat submanifolds in Minkowski spacetime using a similar method. However the Dirac-type operator we used is not the one we introduce in the present paper.…”