Symmetries and conserved quantities for minimal surfaces

Pascal Romon (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We describe here a general method for finding symmetries of minimal surfaces in R^3, namely transformations sending a minimal immersion to another minimal immersion. More specifically we will be looking for infinitesimal symmetries, i.e. vector fields tangent to a Lie group acting on the set of minimal surfaces. Using Nœther's theorem, we derive conserved quantities, i.e. cohomology classes on H_1, that permit us to write so called balancing formulas. Some examples of applications of such balancing formulas are quoted below. Others may be found in [6].

Mots clés: Noether theorem; flux; torque; minimal and constant mean surfaces; jet theory

Domaines: Géométrie différentielle [math.DG]

Pascal Romon. Symmetries and conserved quantities for minimal surfaces. 1997. ⟨hal-00868001⟩