Add to ORKGThe isoperimetric ratio of an embedded surface in $${\mathbb{R}^3}$$ R 3 is defined as the ratio of the area of the surface to power three to the squared enclosed volume. The aim of the present work is to study the minimization of the Willmore energy under fixed isoperimetric ratio when the underlying abstract surface has fixed genus $${g \geqq 0}$$ g ≧ 0 . The corresponding problem in the case of spherical surfaces, that is g=0, was recently solved by Schygulla (see Schygulla, Arch Ration Mech Anal 203:901-941, 2012) with different methods
For a hypersurface in ${\mathbb R}^3$, Willmore flow is defined as the $L^2$--gradient flow of the c...
"Regularity and Singularity for Partial Differential Equations with Conservation Laws". June 3～5, 20...
In this work we present new tools for studying the variations of the Willmore functional of immersed...
The isoperimetric ratio of an embedded surface in R3 is defined as the ratio of the area of the surf...
Inspired by previous work of Kusner and Bauer–Kuwert, we prove a strict inequality between the Willm...
A family of embedded rotationally symmetric tori in the Euclidean 3-space consisting of two opposite...
For a smooth closed embedded planar curve Γ, we consider the minimization problem of the Willmore en...
Abstract. In this paper we study a constrained minimization problem for the Willmore functional. For...
The Willmore energy of a closed surface is defined as the integrated squared mean curvature. It appe...
For a given family of smooth closed curves gamma(1),...,gamma(alpha) subset of R-3 we consider the p...
Let (M, g) be a 3-dimensional Riemannian manifold. The goal of the paper it to show that if P0 ∈ M ...
The goal of the present note is to survey and announce recent results by the authors about existence...
A new formulation for the Euler-Lagrange equation of the Willmore functional for immersed surfaces i...
We consider a closed surface in $\mathbb{R}^3$ evolving by the volume-preserving Willmore flow and p...
In the class of smoothly embedded surfaces of sphere type we prove that the isoperimetric deficit c...
For a hypersurface in ${\mathbb R}^3$, Willmore flow is defined as the $L^2$--gradient flow of the c...
"Regularity and Singularity for Partial Differential Equations with Conservation Laws". June 3～5, 20...
In this work we present new tools for studying the variations of the Willmore functional of immersed...
The isoperimetric ratio of an embedded surface in R3 is defined as the ratio of the area of the surf...
Inspired by previous work of Kusner and Bauer–Kuwert, we prove a strict inequality between the Willm...
A family of embedded rotationally symmetric tori in the Euclidean 3-space consisting of two opposite...
For a smooth closed embedded planar curve Γ, we consider the minimization problem of the Willmore en...
Abstract. In this paper we study a constrained minimization problem for the Willmore functional. For...
The Willmore energy of a closed surface is defined as the integrated squared mean curvature. It appe...
For a given family of smooth closed curves gamma(1),...,gamma(alpha) subset of R-3 we consider the p...
Let (M, g) be a 3-dimensional Riemannian manifold. The goal of the paper it to show that if P0 ∈ M ...
The goal of the present note is to survey and announce recent results by the authors about existence...
A new formulation for the Euler-Lagrange equation of the Willmore functional for immersed surfaces i...
We consider a closed surface in $\mathbb{R}^3$ evolving by the volume-preserving Willmore flow and p...
In the class of smoothly embedded surfaces of sphere type we prove that the isoperimetric deficit c...
For a hypersurface in ${\mathbb R}^3$, Willmore flow is defined as the $L^2$--gradient flow of the c...
"Regularity and Singularity for Partial Differential Equations with Conservation Laws". June 3～5, 20...
In this work we present new tools for studying the variations of the Willmore functional of immersed...