A Weierstrass type representation for minimal surfaces in Sol

Abstract

The normal Gauss map of a minimal surface in the model space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper S normal o normal l"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">o</mml:mi> <mml:mi mathvariant="normal">l</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathrm {Sol}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of solvegeometry is a harmonic map with respect to a certain singular Riemannian metric on the extended complex plane.