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### Open Access Journals

DCDS

We construct two kinds of capillary surfaces by using a perturbation method. Surfaces of first kind are embedded in a solid ball *B* of $\mathbb{R}^3$ with assigned mean curvature function and whose boundary curves lie on $\partial B.$ The contact angle along such curves is a non-constant function. Surfaces of second kind are unbounded and embedded in $\mathbb{R}^3 \setminus \tilde B,$ $\tilde B$ being a deformation of a solid ball in $\mathbb{R}^3.$ These surfaces have assigned mean curvature function and one boundary curve on $\partial \tilde B.$ Also in this case the contact angle along the boundary is a non-constant function.

keywords:
Capillary surfaces
,
Jacobi operator
,
perturbation method
,
contact angle
,
fixed point theorem

DCDS

The aim of this work is to show the existence of
free boundary minimal surfaces of Saddle Tower type which
are embedded in a vertical solid cylinder in $\mathbb{R}^3$ and
invariant with respect to a vertical translation.
The number of boundary curves equals $2l$, $l \ge 2$.
These surfaces come in families depending on one parameter and
they converge to $2l$ vertical stripes having a common
vertical intersection line.
Such surfaces are obtained by perturbing the symmetrically
modified Saddle Tower minimal surfaces.

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