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The Spinor Representation of Minimal Surfaces
Screw die space the projective plane the average curvature functions
2014/12/29
The spinor representation is developed and used to investigate minimal surfaces in R^3 with embedded planar ends. The moduli spaces of planar-ended minimal spheres and real projective planes are deter...
Curved flats and isothermic surfaces.
Bonnet pairs and isothermic surfaces
Four yuan function the theory of differential geometry quaternion Riemann surface figure maps
2014/12/29
In this note we classify all Bonnet pairs on a simply connected domain. Our main intent was to apply what we call a quaternionic function theory to a concrete problem in differential geometry. The ide...
Envelopes and osculates of Willmore surfaces
Holomorphic curves of four yuan projective space close curve will surface
2014/12/25
We view conformal surfaces in the 4-sphere as quaternionic holomorphic curves in quaternionic projective space. By constructing enveloping and osculating curves, we obtain new holomorphic curves in qu...
Sequences of willmore surfaces
Wilmer sequence of holomorphic curves wilmer sphere wilmer torus
2014/12/25
In this paper we develop the theory of Willmore sequences for Willmore surfaces in the 4-sphere. We show that under appropriate conditions this sequence has to terminate. In this case the Willmore sur...
A study on the relation between the smooth structure of a symplectic homotopy K3 surface and its symplectic symmetries is initiated. A measurement of exoticness of a symplectic homotopy K3 surface is ...
Motivated by Segal's axiom of conformal field theory, we do a survey on geometrical random fields. We do a history in order to arrive at a field theoretical analog of Klauder's quantization in Hamilto...