14 Feb
2008
14 Feb
'08
1:19 p.m.
Fred writes: << On 2/14/08, [I] wrote: << ... In any case, the impossibility of a bijection H^2 -> H^2 that increases all distances by a factor of (say) 2 brings up an interesting question: Can one quantify just how close one can get to such a map?
In particular, can one choose constants c1, c2 both > 1 such that c1 <= |f(x) - f(y)| / |x - y| <= c2 ?>>
Good question. (My guess is no, because lengths pushed a distance R away from a point increase in an exponential manner as a function of R.) --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele