Related papers: Minimal surfaces - variational theory and applicat…
In this thesis, we present various contributions to the study of free boundary minimal surfaces. After introducing some basic tools and discussing some delicate aspects related to the definition of Morse index when allowing for a contact…
We prove a version of the classical Runge and Mergelyan uniform approximation theorems for non-orientable minimal surfaces in Euclidean 3-space R3. Then, we obtain some geometric applications. Among them, we emphasize the following ones: 1.…
In this paper, we derive the first variation formulas for surfaces in 3-dimensional Euclidean space by using the ``strain-displacement relations'' known in thin shell theory. For applications to architectural surface design, we focus on the…
The study of embedded minimal surfaces in $\RR^3$ is a classical problem, dating to the mid 1700's, and many people have made key contributions. We will survey a few recent advances, focusing on joint work with Tobias H. Colding of MIT and…
Level proximal subdifferential was introduced by Rockafellar recently for studying proximal mappings of possibly nonconvex functions. In this paper a systematic study of level proximal subdifferential is given. We characterize variational…
This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate…
An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.
This article explains a program to study complete and properly embedded minimal surfaces in $\mathbb{R}^3$ developed jointly with W.H. Meeks and A. Ros in the last three decades. It follows closely the structure of my invited ICM talk with…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
Minimal surfaces with planar curvature lines in the Euclidean space have been studied since the late 19th century. On the other hand, the classification of maximal surfaces with planar curvature lines in the Lorentz-Minkowski space has only…
For a surface immersed in a three-dimensional space endowed with a norm instead of an inner product, one can define analogous concepts of curvature and metric. With these concepts in mind, various questions immediately appear. The aim of…
We associate curves of isotropic, Lagrangian and coisotropic subspaces to higher order, one parameter variational problems. Minimality and conjugacy properties of extremals are described in terms of these curves.
The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the…
We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group.…
Diffeology extends differential geometry to spaces beyond smooth manifolds. This paper explores diffeology's key features and illustrates its utility with examples including singular and quotient spaces, and applications in symplectic…
We consider developable surfaces along the singular set of a swallowtail which are considered to be flat approximations of the swallowtail. For the study of singularities of such developable surfaces, we introduce the notion of Darboux…
It is pointed out that despite of the non-linearity of the underlying equations, there do exist rather general methods that allow to generate new minimal surfaces from known ones.
We study toric varieties over an arbitrary field with an emphasis on toric surfaces in the Merkurjev-Panin motivic category of "K-motives". We explore the decomposition of certain toric varieties as K-motives into products of central simple…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
We examine some common features of minimal surfaces, nonzero constant mean curvature surfaces and marginally outer trapped surfaces, concerning their stability and rigidity, and consider some applications to Riemannian geometry and general…