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- Title
A duality for prescribed mean curvature graphs in Riemannian and Lorentzian Killing submersions.
- Authors
Del Prete, Andrea; Lee, Hojoo; Manzano, José Miguel
- Abstract
We develop a conformal duality for space‐like graphs in Riemannian and Lorentzian three‐manifolds that admit a Riemannian submersion over a Riemannian surface whose fibers are the integral curves of a Killing vector field, which is time‐like in the Lorentzian case. The duality swaps mean curvature and bundle curvature and sends the length of the Killing vector field to its reciprocal while keeping invariant the base surface. We obtain two consequences of this result. On the one hand, we find entire graphs in Lorentz–Minkowski space L3$\mathbb {L}^3$ with prescribed mean curvature a bounded function H∈C∞(R2)$H\in \mathcal {C}^\infty (\mathbb {R}^2)$ with bounded gradient. On the other hand, we obtain conditions for the existence and nonexistence of entire graphs which are related to a notion of the critical mean curvature.
- Subjects
CURVATURE; VECTOR fields
- Publication
Mathematische Nachrichten, 2024, Vol 297, Issue 5, p1581
- ISSN
0025-584X
- Publication type
Article
- DOI
10.1002/mana.202300282