Wikipedia:Reference desk/Archives/Mathematics/2017 November 3

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November 3

Riemann surface with analytic mapping to hyperbolic surface is hyperbolic

If $f:R\to S$ is a non-constant analytic mapping between two Riemann surfaces, and Green's function $g_{S}$ exists, then I want to know why $g_{R}(p,q)\leq g_{S}(f(p),f(q))$ for all $p,q$. I did not find this in standard texts. In case $f'$ is nowhere-zero I think it can be proved using the local homeomorphism of $f$ that guarantees local coordinate functions are carried to local coordinate functions. How can it be done in general? By definition of Green's function we may take the supremum of subharmonic functions on the punctured surface with compact support and logarithmic pole.--אדי פ' (talk) 13:14, 3 November 2017 (UTC)

Fermat's Theorem of Maxima in the Original

Hi all,

This is a long shot, but where might I be able to find the Latin text where Fermat proved his theorem about stationary points: https://en.wikipedia.org/wiki/Fermat%27s_theorem_(stationary_points) — Preceding unsigned comment added by 140.233.166.175 (talk) 23:25, 3 November 2017 (UTC)

It's available on the French WikiSource site, at fr:Œuvres_de_Fermat/I/Maxima_et_Minima. Tevildo (talk) 13:53, 4 November 2017 (UTC)

Also in Google Books here. (Well, I only looked at the first few lines to confirm that it seems to be the same text.) --69.159.60.147 (talk) 04:19, 5 November 2017 (UTC)