An isothermal parameterization of a regular surface 
is a parameterization whose coordinate tangent
vectors are orthogonal and have the same length. Equivalently, its first
fundamental form has the form 
for some positive function 
.
For 
,
define
 |
where 
are the coordinate functions of 
. The isothermal conditions are equivalent to
 |
and the surface is a minimal surface iff the functions 
are harmonic. Equivalently,
each 
is analytic.
