Functionals involving surface curvature are important across a range of scientific disciplines,
and their extrema are representative of physically meaningful objects such as atomic lattices …

Functionals involving surface curvature are frequently encountered when modeling the
behavior of important biological structures such as lipid membranes. To better understand …

In this paper we study a Generalized Willmore flow for graphs and its numerical applications.
First, we derive the time dependent equation which describes the geometric evolution of a …

Variational calculus has played a very important role in mathematics and physical sciences.
Given an energy functional, the critical points of the first variation satisfy the Euler-Lagrange …

The main goal of this paper is to use the theory of exterior differential forms in deriving
variations of the deformed Willmore energy in space forms and study the minimizers of the …

In this article, we revisit some results published by several mathematicians regarding
existence and non-existence of doubly connected minimal surfaces between two circles in …

In this chapter we give analytical representations of Willmore and generalized Willmore
(Helfrich) surfaces. All cylindrical surfaces of that type are described. Some special families …

In this paper we study a Generalized Willmore flow for graphs and its numerical applications.
First, we derive the time dependent equation which describes the geometric evolution of a …

The work is concerned with a special family of axially symmetric surfaces providing local
extrema to the so-called Willmore functional, which assigns to each surface its total squared …

Space forms ABPT Page 1 Willmore-type energies and Willmore-type surfaces in space forms
- Preliminary Version Bhagya Athukorallage∗1, Giorgio Bornia†1, Thanuja Paragoda‡1 and …