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Abstract By means of the algebraic, analysis, convex geometry, computer, and inequality theories we establish the following isoperimetric inequality in the centered 2-surround system S ( 2 ) { P , Γ , l } $S^{(2)} \{P,\varGamma ,l \}$ : ( 1 | Γ | ∮ Γ r ¯ P p ) 1 / p ⩽ | Γ | 4 π sin l π | Γ | [ csc l π | Γ | + cot 2 l π | Γ | ln ( tan l π | Γ | + sec l π | Γ | ) ] , ∀ p ⩽ − 2 . $$\begin{aligned}& \biggl(\frac{1}{|\varGamma |} \oint_{\varGamma }\bar{r}_{P}^{p} \biggr)^{1/p}\leqslant\frac{|\varGamma |}{4\pi}\sin\frac{l\pi}{|\varGamma |} \biggl[ \csc \frac{l\pi}{|\varGamma |}+\cot^{2} \frac{l\pi}{|\varGamma |} \ln \biggl(\tan \frac{l\pi}{|\varGamma |}+\sec\frac{l\pi}{|\varGamma |} \biggr) \biggr], \\& \quad \forall p\leqslant -2. \end{aligned}$$ As an application of the inequality in space science, we obtain the best lower bounds of the mean λ-gravity norm ∥ F λ ( Γ , P ) ∥ ‾ $\overline{\Vert {\mathbf{F}}_{\lambda} ( \varGamma ,P )\Vert }$ as follows: ∥ F λ ( Γ , P ) ∥ ‾ ≜ 1 | Γ | ∮ Γ 1 ∥ A − P ∥ λ ⩾ ( 2 π | Γ | ) λ , ∀ λ ⩾ 2 . $$\overline{\bigl\Vert {\mathbf{F}}_{\lambda} ( \varGamma ,P )\bigr\Vert } \triangleq\frac{1}{|\varGamma |} \oint_{\varGamma }\frac{1}{\|A-P\|^{\lambda }}\geqslant \biggl(\frac{2\pi}{|\varGamma |} \biggr)^{\lambda},\quad \forall \lambda\geqslant2. $$