Surfaces of constant Gauβ curvature and of arbitrary genus

In section 3, we prove two properties for surfaces with B.I.C.: one result concerns the volume of balls (by analogy with the case of smooth Riemannian metrics, when one has a control

As already mentioned, the objective of this paper is to consider surfaces (with boundary) with corners on their boundary and to study the existence problem of conformal metrics

There exists c > 0 such that, if Γ is a closed curve of degree d immersed in Ω with constant geodesic curvature k > 0, then there exists p, a critical point of the Gauss

FUCHS, A general existence theorem for integral currents with prescribed mean curvature form, in Boll. FEDERGER, The singular set of area minimizing rectifiable

Analogous boundary regularity questions for solutions of the nonpara- metric least area problem were studied by Simon [14]. 2) arises in a similar fashion as for

3-dimensional manifold with boundary M which prevents interior contact between minimizing surfaces in M and the boundary of M unless the surface is totally contained

In this section we construct an explicitly known family of surfaces of constant mean curvature which will serve as comparison surfaces to give us... These

The result of Finn cited above presents a natural analogue of that theorem for surfaces of prescribed mean curvature; the present paper in turn extends the result to