Year: 2026
Type: article
Abstract: Our aim in this paper is to investigate geometric conditions which guarantee the nonexistence of spacelike solitons of the r -th mean curvature flow (shortly, r -MCF) in a pp-wave spacetime, namely, a $$(n+1)$$ ( n + 1 ) -dimensional connected Lorentzian manifold admitting a parallel lightlike vector field, where $$n\ge 2$$ n ≥ 2 and $$r\in \{1,\ldots ,n\}$$ r ∈ { 1 , … , n } . Our approach is based on three main analytical frameworks: a Liouville type result, a maximum principle for complete noncompact Riemannian manifolds with polynomial volume growth or satisfying a certain convergence at infinity, and a suitable version of the Omori-Yau maximum principle. Furthermore, we also exhibit nice nontrivial examples of spacelike solitons of the r -MCF in a pp-wave spacetime, showing that the main hypotheses that we assume in our nonexistence results are, indeed, necessary.
Source: Letters in Mathematical Physics
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
Awards: G22113365, G304002239, G3189066738, G5956834982
OpenAlex ID: W7204265898