2022/08/13 by King Ming Lam, Lam, King Ming · 1 citation
Mathematics · #Mathematics and Applications #Point processes and geometric inequalities #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2208.06736
We establish various qualitative properties of liquid Lane-Emden stars in ℝd, including bounds for its density profile ρ and radius R. Using them we prove that against radial perturbations, the liquid Lane-Emden stars are linearly stable when γ≥ 2(d-1)/d; linearly stable when γ<2(d-1)/d for stars with small relative central density ρ(0)-ρ(R); and linearly unstable when γ<2(d-1)/d for stars with large central density. Such dependence on central density is not seen in the gaseous Lane-Emden stars.