Laurent Hauswirth

The geometry of finite topology Bryant surfaces

We prove that in the three dimensional hyperbolic space H(3) the properly embedded constant mean curvature one surfaces with finite topology are of finite total curvature and each ends are regular. This imply in particular that the hrosphere is the only properly embedded simply connected constant mean curvature one surface in H(3).

INFINITE BOUNDARY VALUE PROBLEMS FOR CONSTANT MEAN CURVATURE GRAPHS IN H2 × R AND S2 × R

We extend the classical existence and uniqueness theory of Jenkins-Serrin

Embedded minimal ends of finite type

(H=0)

The periodic isoperimetric problem

and Spruck

GENERAL CURVATURE ESTIMATES FOR STABLE H-SURFACES IMMERSED INTO A SPACE FORM

(H>0)

Deformations of constant mean curvature-1/2 surfaces in

for the constant mean curvature equation over a domain in

\mathbb{H}^2 \times \mathbb{R}

R^2

with vertical ends at infinity

, to domains in

On mean-convex Alexandrov embedded surfaces in the 3-sphere

H^2

Harmonic maps with prescribed degrees on the boundary of an annulus and bifurcation of catenoids

or