Related papers: Minimal surfaces - variational theory and applicat…
Minimal surfaces in a Riemannian manifold $M^n$ are surfaces which are stationary for area: the first variation of area vanishes. In this paper we focus on surfaces of the topological type of the real projective plane $\R P^2$. We show that…
We survey - by means of 20 examples - the concept of varifold, as generalised submanifold, with emphasis on regularity of integral varifolds with mean curvature, while keeping prerequisites to a minimum. Integral varifolds are the natural…
Real Legendrian subvarieties are classical objects of differential geometry and classical mechanics and they have been studied since antiquity. However, complex Legendrian subvarieties are much more rigid and have more exceptional…
We introduce the notion of a minimal Lagrangian connection on the tangent bundle of a manifold and classify all such connections in the case where the manifold is a compact oriented surface of non-vanishing Euler characteristic. Combining…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
Harmonic mappings have long intrigued researchers due to their intrinsic connection with minimal surfaces. In this paper, we investigate shearing of two distinct classes of univalent conformal mappings which are convex in horizontal…
The theory of surfaces in Euclidean space can be naturally formulated in the more general context of Legendre surfaces into the space of contact elements. We address the question of deformability of Legendre surfaces with respect to the…
An increasingly important area of interest for mathematicians is the study of Abelian differentials. This growing interest can be attributed to the interdisciplinary role this subject plays in modern mathematics, as various problems of…
Solving the Plateau problem means to find the surface with minimal area among all surfaces with a given boundary. Part of the problem actually consists of giving a suitable definition to the notions of 'surface', 'area' and 'boundary'. In…
Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are…
This paper introduces a geometrically constrained variational problem for the area functional. We consider the area restricted to the langrangian surfaces of a Kaehler surface, or, more generally, a symplectic 4-manifold with suitable…
Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…
We construct new examples of immersed minimal surfaces with catenoid ends and finite total curvature, of both genus zero and higher genus. In the genus zero case, we classify all such surfaces with at most $2n+1$ ends, and with symmetry…
We prove that the Gauss curvature and the curvature of the normal connection of any minimal surface in the four dimensional Euclidean space satisfy an inequality, which generates two classes of minimal surfaces: minimal surfaces of general…
These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the…
Surfaces admitting flows all whose orbits are dense are called minimal. Minimal orientable surfaces were characterized by J.C. Beni\`{e}re in 1998, leaving open the nonorientable case. This paper fills this gap providing a characterization…
After a historical discussion of classical uniformisation results for Riemann surfaces, of problems appearing in higher dimensions, and of uniformisation results for projective manifolds with trivial or ample canonical bundle, we introduce…
We consider compact connected minimal surfaces, with a pair of boundary curves (not necessarily convex) in distinct planes, that have least-area amongst all orientable surfaces with the same boundary. When the planes containing these two…
We study minimal surfaces which arise in wetting and capillarity phenomena. Using conformal coordinates, we reduce the problem to a set of coupled boundary equations for the contact line of the fluid surface, and then derive simple…
Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. This branch of differential geometry is still so far from being exhausted; only a small portion of an…