22 citations · 63 across the 19 of their papers we have counts for
19 papers
Delaunay surfaces with free boundary on the unit -sphere
Eric Lang, Christian Scharrer
We characterize all symmetric, embedded surfaces of revolution with constant mean curvature that meet the unit sphere orthogonally. It is well known that there exists a unique free…
Existence and convergence of the area-constrained elastic flow
Florian Hauser, Christian Scharrer, Alexander West
We study the evolution of plane closed curves with fixed area moving by the negative -gradient of their elastic energy. For smooth initial data, we establish local and global…
Bubble classification of immersions at the boundary of the moduli space with Willmore energy
Christian Scharrer, Manuel Schlierf, Alexander West
We study the asymptotic bubbling behavior of sequences of weak genus- immersions with diverging conformal classes and limiting Willmore energy of . After applying suitable M…
Energy quantization for constrained Willmore surfaces
Christian Scharrer, Alexander West
We establish an energy quantization for constrained Willmore surfaces, where the constraints are given by area, volume, and total mean curvature, assuming that the underlying confo…
Gradient flow dynamics for cell membranes in the Canham-Helfrich model
Fabian Rupp, Christian Scharrer, Manuel Schlierf
The energetically most efficient way how a deformed red blood cell regains equilibrium is mathematically described by the gradient flow of the Canham-Helfrich functional, including…
Global regularity of integral 2-varifolds with square integrable mean curvature
Fabian Rupp, Christian Scharrer
We provide sharp sufficient criteria for an integral -varifold to be induced by a -conformal immersion of a smooth surface. Our approach is based on a fine analysis of…
On the minimization of the Willmore energy under a constraint on total mean curvature and area
Christian Scharrer, Alexander West
Motivated by a model for lipid bilayer cell membranes, we study the minimization of the Willmore functional in the class of oriented closed surfaces with prescribed total mean curv…
Properties of surfaces with spontaneous curvature
Christian Scharrer
A model describing cell membranes as optimal shapes with regard to the -deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is s…
Short closed geodesics and the Willmore energy
Marius Müller, Fabian Rupp, Christian Scharrer
We prove a lower bound on the length of closed geodesics for spheres with Willmore energy below . The energy threshold is optimal and the inequality cannot be extended to surfa…
Diameter estimates for surfaces in conformally flat spaces
Marco Flaim, Christian Scharrer
The aim of this paper is to give an upper bound for the intrinsic diameter of a surface with boundary immersed in a conformally flat three dimensional Riemannian manifold in terms…
A priori bounds for geodesic diameter. Part II. Fine connectedness properties of varifolds
Ulrich Menne, Christian Scharrer
For varifolds whose first variation is representable by integration, we introduce the notion of indecomposability with respect to locally Lipschitzian real valued functions. Unlike…
A priori bounds for geodesic diameter. Part I. Integral chains with coefficients in a complete normed commutative group
Ulrich Menne, Christian Scharrer
As service to the community, we provide - for Euclidean space - a basic treatment of locally rectifiable chains and of the complex of locally integral chains. In this setting, we m…
Li-Yau inequalities for the Helfrich functional and applications
Fabian Rupp, Christian Scharrer
We prove a general Li-Yau inequality for the Helfrich functional where the spontaneous curvature enters with a singular volume type integral. In the physically relevant cases, this…
Some geometric inequalities for varifolds on Riemannian manifolds based on monotonicity identities
Christian Scharrer
Using Rauch's comparison theorem, we prove several monotonicity inequalities for Riemannian submanifolds. Our main result is a general Li-Yau inequality which is applicable in any…
Embedded Delaunay tori and their Willmore energy
Christian Scharrer
A family of embedded rotationally symmetric tori in the Euclidean 3-space consisting of two opposite signed constant mean curvature surfaces that converge as varifolds to a double…
A strict inequality for the minimisation of the Willmore functional under isoperimetric constraint
Andrea Mondino, Christian Scharrer
Inspired by previous work of Kusner and Bauer-Kuwert, we prove a strict inequality between the Willmore energies of two surfaces and their connected sum in the context of isoperime…
Existence and Regularity of Spheres Minimising the Canham-Helfrich Energy
Andrea Mondino, Christian Scharrer
We prove existence and regularity of minimisers for the Canham-Helfrich energy in the class of weak (possibly branched and bubbled) immersions of the -sphere. This solves (the s…
A priori bounds for geodesic diameter. Part III. A Sobolev-Poincaré inequality and applications to a variety of geometric variational problems
Ulrich Menne, Christian Scharrer
Based on a novel type of Sobolev-Poincaré inequality (for generalised weakly differentiable functions on varifolds), we establish a finite upper bound of the geodesic diameter of g…
An isoperimetric inequality for diffused surfaces
Ulrich Menne, Christian Scharrer
For general varifolds in Euclidean space, we prove an isoperimetric inequality, adapt the basic theory of generalised weakly differentiable functions, and obtain several Sobolev ty…