Test of number-swapping

This is a repeat of the first section but with numbers in theorem heads swapped to the left.

Ahlfors' Lemma gives the principal criterion for obtaining lower bounds on the Kobayashi metric.

Ahlfors' Lemma 2 Let ds² = h(z) $\lvert$ dz $\rvert^{2}_{}$ be a Hermitian pseudo-metric on D_r, h∈C²(D_r), with ω the associated (1, 1)-form. If Ric $\nolimits$ ω≥ω on D_r, then ω≤ω_r on all of D_r (or equivalently, ds²≤ds_r²).

Lemma 2.1 (negatively curved families) Let {ds₁²,..., ds_k²} be a negatively curved family of metrics on D_r, with associated forms ω¹, ..., ω^k. Then ωⁱ≤ω_r for all i.

Then our main theorem:

Theorem 2.1 Let d_max and d_min be the maximum, resp. minimum distance between any two adjacent vertices of a quadrilateral Q. Let σ be the diagonal pigspan of a pig P with four legs. Then P is capable of standing on the corners of Q iff

σ≥ $\displaystyle \sqrt{{d_{\max}^2+d_{\min}^2}}$ .

(2)

Corollary 2.2 Admitting reflection and rotation, a three-legged pig P is capable of standing on the corners of a triangle T iff () holds.