$L^2$-decomposition of the second fundamental form of a hypersurface in the study of the general relativistic vacuum constraint equations

Sergey E. Stepanov; Irina I. Tsyganok

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arXiv · 2406.04760

$L^2$-decomposition of the second fundamental form of a hypersurface in the study of the general relativistic vacuum constraint equations

Sergey E. Stepanov·Irina I. Tsyganok

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Abstract

In present article, we consider a $L^2$-orthogonal decomposition of the second fundamental form of a closed spacelike hypersurface in a Lorentzian spacetime and its applications to the study of some algebraic-differential properties of the general relativistic vacuum constraint equations. For the study we will use the well-known Ahlfors Laplacian.

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Sergey E. Stepanov, Irina I. Tsyganok. 2024-06-07. $L^2$-decomposition of the second fundamental form of a hypersurface in the study of the general relativistic vacuum constraint equations. https://arxiv.org/abs/2406.04760

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