We study immersed surfaces in R$^{3}$ that are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary and when the boundary is contained in a line. In both cases we derive weak forms of the resulting free boundary conditions and prove regularity by reflection
For a hypersurface in ${\mathbb R}^3$, Willmore flow is defined as the $L^2$--gradient flow of the c...
We consider a closed surface in $\mathbb{R}^3$ evolving by the volume-preserving Willmore flow and p...
The first variation formula and Euler-Lagrange equations for Willmore-like surfaces in Riemannian 3-...
A new formulation for the Euler-Lagrange equation of the Willmore functional for immersed surfaces i...
In this work we present new tools for studying the variations of the Willmore functional of immersed...
In this paper we prove a convergence result for sequences of Willmore immersions with simple minimal...
Let S ⊂ R2 be a bounded domain with boundary of class C ∞ and let gij = δij denote the flat metric o...
"Regularity and Singularity for Partial Differential Equations with Conservation Laws". June 3～5, 20...
Using techniques both of non linear analysis and geometric measure theory, we prove existence of min...
Abstract: A new formulation for the Euler-Lagrange equation of the Will-more functional for immersed...
We show the existence of a local foliation of a three dimensional Riemannian manifold by critical po...
A surface $x:M\to S^n$ is called a Willmore surface if it is a critical surface of the Willmore func...
We give an asymptotic lower bound for the Willmore energy of weak immersions with degenerating confo...
The goal of the present note is to survey and announce recent results by the authors about existence...
The isoperimetric ratio of an embedded surface in $${\mathbb{R}^3}$$ R 3 is defined as the ratio of ...
For a hypersurface in ${\mathbb R}^3$, Willmore flow is defined as the $L^2$--gradient flow of the c...
We consider a closed surface in $\mathbb{R}^3$ evolving by the volume-preserving Willmore flow and p...
The first variation formula and Euler-Lagrange equations for Willmore-like surfaces in Riemannian 3-...
A new formulation for the Euler-Lagrange equation of the Willmore functional for immersed surfaces i...
In this work we present new tools for studying the variations of the Willmore functional of immersed...
In this paper we prove a convergence result for sequences of Willmore immersions with simple minimal...
Let S ⊂ R2 be a bounded domain with boundary of class C ∞ and let gij = δij denote the flat metric o...
"Regularity and Singularity for Partial Differential Equations with Conservation Laws". June 3～5, 20...
Using techniques both of non linear analysis and geometric measure theory, we prove existence of min...
Abstract: A new formulation for the Euler-Lagrange equation of the Will-more functional for immersed...
We show the existence of a local foliation of a three dimensional Riemannian manifold by critical po...
A surface $x:M\to S^n$ is called a Willmore surface if it is a critical surface of the Willmore func...
We give an asymptotic lower bound for the Willmore energy of weak immersions with degenerating confo...
The goal of the present note is to survey and announce recent results by the authors about existence...
The isoperimetric ratio of an embedded surface in $${\mathbb{R}^3}$$ R 3 is defined as the ratio of ...
For a hypersurface in ${\mathbb R}^3$, Willmore flow is defined as the $L^2$--gradient flow of the c...
We consider a closed surface in $\mathbb{R}^3$ evolving by the volume-preserving Willmore flow and p...
The first variation formula and Euler-Lagrange equations for Willmore-like surfaces in Riemannian 3-...
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