On an inverse curvature flow in two-dimensional space forms

New weighted geometric inequalities for hypersurfaces in space forms

“…Remark 1.6. Weighted geometric inequalities of the same kind for curves (that is, for 𝑛 = 1) in 2-dimensional space form were proved recently by the first author with Kwong, Wheeler and Wheeler [20].…”

“…By showing that the curvature integral $$\int _{M_t}\Phi E_1(\kappa )d\mu _t$$ is non‐increasing along convex solution of the flow (1.15), we obtain the inequality (1.16) for convex hypersurfaces. Remark Weighted geometric inequalities of the same kind for curves (that is, for $$n=1$$) in 2‐dimensional space form were proved recently by the first author with Kwong, Wheeler and Wheeler [20]. …”