7 research outputs found
Geometry of complete minimal surfaces at infinity and the Willmore index of their inversions
We study complete minimal surfaces in with finite total
curvature and embedded planar ends. After conformal compactification via
inversion, these yield examples of surfaces stationary for the Willmore bending
energy . In codimension one, we prove
that the -Morse index for any inverted minimal sphere with
such ends is exactly , completing previous
work. We consider several geometric properties - for example, the property that
all asymptotic planes meet at a single point - of these minimal surfaces
and explore their relation to the -Morse index of their inverted
surfaces.Comment: Comments welcom
A posteriori error estimates for wave maps into spheres
We provide a posteriori error estimates in the energy norm for temporal
semi-discretisations of wave maps into spheres that are based on the angular
momentum formulation. Our analysis is based on novel weak-strong stability
estimates which we combine with suitable reconstructions of the numerical
solution. Numerical experiments are presented that confirm that our error
estimates are formally optimal until the solution develops singularities