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pro vyhledávání: '"Scharrer, Christian"'
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 a spontaneous curvature and the conservation of surface area and encl
Externí odkaz:
http://arxiv.org/abs/2408.07493
Autor:
Rupp, Fabian, Scharrer, Christian
We provide sharp sufficient criteria for an integral $2$-varifold to be induced by a $W^{2,2}$-conformal immersion of a smooth surface. Our approach is based on a fine analysis of the Hausdorff density for $2$-varifolds with critical integrability of
Externí odkaz:
http://arxiv.org/abs/2404.12136
Autor:
Scharrer, Christian, West, Alexander
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 curvature, prescribed area, and prescribed genus. Adapting methods previou
Externí odkaz:
http://arxiv.org/abs/2403.14579
Autor:
Scharrer, Christian
A model describing cell membranes as optimal shapes with regard to the $L^2$-deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is shown that the corresponding energy functional is lower semi-continuous
Externí odkaz:
http://arxiv.org/abs/2310.19935
We prove a lower bound on the length of closed geodesics for spherical surfaces with Willmore energy below $6\pi$. The energy threshold is optimal and there is no comparable result for surfaces of higher genus. We also discuss consequences for the in
Externí odkaz:
http://arxiv.org/abs/2304.01809
Autor:
Flaim, Marco, Scharrer, Christian
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 of the integral of the mean curvature and of the length of its boundar
Externí odkaz:
http://arxiv.org/abs/2303.09885
Autor:
Menne, Ulrich, Scharrer, Christian
For varifolds whose first variation is representable by integration, we introduce the notion of indecomposability with respect to locally Lipschitzian real valued functions. Unlike indecomposability, this weaker connectedness property is inherited by
Externí odkaz:
http://arxiv.org/abs/2209.05955
Autor:
Menne, Ulrich, Scharrer, Christian
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 may beneficially develop the idea of a complete normed commutative grou
Externí odkaz:
http://arxiv.org/abs/2206.14046
Autor:
Rupp, Fabian, Scharrer, Christian
Publikováno v:
Calc. Var. Partial Differential Equations 62, 45 (2023)
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 term can be converted into an explicit energy threshold that guarante
Externí odkaz:
http://arxiv.org/abs/2203.12360
Autor:
Scharrer, Christian
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 Riemannian manifold whose sectional curvature is bounded above (possib
Externí odkaz:
http://arxiv.org/abs/2105.13211