# Uniqueness theorems for Willmore surfaces with fixed and free boundaries

@article{Palmer2000UniquenessTF, title={Uniqueness theorems for Willmore surfaces with fixed and free boundaries}, author={Bennett Palmer}, journal={Indiana University Mathematics Journal}, year={2000}, volume={49}, pages={0-0} }

## 24 Citations

### Uniqueness for the homogeneous Dirichlet Willmore boundary value problem

- MathematicsAnnals of Global Analysis and Geometry
- 2012

We give a sufficient condition for curves on a plane or on a sphere such that if these give the boundary of a Willmore surface touching tangentially along the boundary the plane or the sphere…

### Uniqueness for the homogeneous Dirichlet Willmore boundary value problem

- Mathematics
- 2012

We give a sufficient condition for curves on a plane or on a sphere such that if these give the boundary of a Willmore surface touching tangentially along the boundary the plane or the sphere…

### Stationary surfaces with boundaries

- MathematicsAnnals of Global Analysis and Geometry
- 2022

This article investigates stationary surfaces with boundaries, which arise as the critical points of functionals dependent on curvature. Precisely, a generalized “bending energy” functional…

### On the Bj\"orling problem for Willmore surfaces

- Mathematics
- 2014

We solve the analogue of Bj\"orling's problem for Willmore surfaces via a harmonic map representation. For the umbilic-free case the problem and solution are as follows: given a real analytic curve…

### Gap phenomena for a class of fourth-order geometric differential operators on surfaces with boundary

- Mathematics
- 2013

Abstract. In this paper we establish a gap phenomenon for immersed surfaces with arbitrary codimension, topology and boundaries that satisfy one of a family of systems of fourth-order anisotropic…

### The Euler–Helfrich functional

- MathematicsCalculus of Variations and Partial Differential Equations
- 2022

We investigate equilibrium configurations for surface energies which contain the squared L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…

### Minimizing Configurations for Elastic Surface Energies with Elastic Boundaries

- Materials ScienceJournal of Nonlinear Science
- 2021

We study critical surfaces for a surface energy which contains the squared L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

### Minimizing Configurations for Elastic Surface Energies with Elastic Boundaries

- MathematicsJ. Nonlinear Sci.
- 2021

We study critical surfaces for a surface energy which contains the squared $$L^2$$ L 2 norm of the difference of the mean curvature H and the spontaneous curvature $$c_o$$ c o , coupled to the…

### Regarding the Euler–Plateau problem with elastic modulus

- MathematicsAnnali di Matematica Pura ed Applicata (1923 -)
- 2021

We study equilibrium configurations for the Euler–Plateau energy with elastic modulus, which couples an energy functional of Euler–Plateau type with a total curvature term often present in models for…

### On the Plateau–Douglas problem for the Willmore energy of surfaces with planar boundary curves

- MathematicsESAIM: Control, Optimisation and Calculus of Variations
- 2021

For a smooth closed embedded planar curve Γ, we consider the minimization problem of the Willmore energy among immersed surfaces of a given genus 𝔤 ≥ 1 having the curve Γ as boundary, without any…