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Joel Spruck

Publications and source records attributed to Joel Spruck.

23 records · Page 2Linked to original sources
arXiv2010

Hypersurfaces of constant curvature in Hyperbolic space

We show that for a very general and natural class of curvature functions, the problem of finding a complete strictly convex hypersurface satisfying f(κ) = σ over (0,1) with a prescribed asymptotic boundary Γ at infinity has at least one solution which is a "vertical graph" over the interior (or the exterior) of Γ. There is uniqueness for a certain subclass of these curvature functions and as σ varies between 0 and 1, these hypersurfaces foliate the two components of the complement of the hyperbolic convex hull of Γ.

math.AP↗
arXiv2010

Charged cosmological dust solutions of the coupled Einstein and Maxwell equations

It is well known through the work of Majumdar, Papapetrou, Hartle, and Hawking that the coupled Einstein and Maxwell equations admit a static multiple blackhole solution representing a balanced equilibrium state of finitely many point charges. This is a result of the exact cancellation of gravitational attraction and electric repulsion under an explicit condition on the mass and charge ratio. The resulting system of particles, known as an extremely charged dust, gives rise to examples of spacetimes with naked singularities. In this paper, we consider the continuous limit of the Majumdar--Papapetrou--Hartle--Hawking solution modeling a space occupied by an extended distribution of extremely charged dust. We show that for a given smooth distribution of matter of finite ADM mass there is a continuous family of smooth solutions realizing asymptotically flat space metrics.

gr-qc↗
arXiv2008

Hypersurfaces of Constant Curvature in Hyperbolic Space II

We find complete hypersurfaces of constant curvature in hyperbolic space with a prescribed asymptotic boundary at infinity for a general class of (elliptic) curvature functions which includes the higher order mean curvatures and their curvature quotients.

math.DG↗
arXiv2008

Proof of the Julia-Zee Theorem

It is a well accepted principle that finite-energy static solutions in the classical relativistic gauge field theory over the $(2+1)$-dimensional Minkowski spacetime must be electrically neutral. We call such a statement the Julia--Zee theorem. In this paper, we present a mathematical proof of this fundamental structural property.

hep-th↗