Related papers: On the Equilibrium Shape of Erythrocytes
This review reports some theoretical results on the Geometry of membranes. The governing equations to describe equilibrium configurations of lipid vesicles, lipid membranes with free edges, and chiral lipid membranes are derived from the…
This research aimed to introduce the concept of harmonically m-concave set-valued functions, which is obtained from the combination of two definitions: harmonically m-concave functions and set-valued functions. In this work some properties…
In this paper, we give an overview of some results concerning best and random approximation of convex bodies by polytopes. We explain how both are linked and see that random approximation is almost as good as best approximation.
Rigidity transitions in simple models of confluent cells have been a powerful organizing principle in understanding the dynamics and mechanics of dense biological tissue. In this work we explore the interplay between geometry and rigidity…
Constructive properties of uniform convexity, strict convexity, near convexity, and metric convexity in real normed linear spaces are considered. Examples show that certain classical theorems, such as the existence of points of osculation,…
We study the equilibrium shape of liquid drops minimizing the fractional perimeter under the action of a potential energy. We prove, with a quantitative estimate, that the small volume minimizers are convex and uniformly close to a ball.
Phagocytosis and receptor-mediated endocytosis are vitally important particle uptake mechanisms in many cell types, ranging from single-cell organisms to immune cells. In both processes, engulfment by the cell depends critically on both…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
Some inequalities for different types of convexity are established.
Collective cell motions underlie structure formation during embryonic development. Tissues exhibit emergent multicellular characteristics such as jamming, rigidity transitions, and glassy dynamics, but there remain questions about how those…
A method of Gabber (2002) produces unramified cohomology classes in the products of certain varieties with an elliptic curve. The connection between third unramified cohomology and integral Hodge conjecture for codimension 2 cycles (2012,…
In this paper we prove that the Euler-Lagrange equations for the limit shape for the inhomogeneous six vertex model on a cylinder have infinitely many conserved quantities.
A simple kinetic model of a two-component deformable and reactive bilayer is presented. The two differently shaped components are interconverted by a nonequilibrium reaction, and a phenomenological coupling between local composition and…
The harmonicity condition of the curvature 2-form of a pseudo- Riemannian manifold is formulated on the basis of annulment of this form by the de Rham-Lichnerowicz Laplacian. The following theorem is proved: The curvature 2-form of any…
It is shown that tube sets over amoebas of algebraic varieties (and, more generally, of almost periodic holomorphic chains) of dimension q are q-pseudoconcave in the sense of Rothstein. This is a direct consequence of a representation of…
For convex partitions of a convex body $B$ we prove that we can put a homothetic copy of $B$ into each set of the partition so that the sum of homothety coefficients is $\ge 1$. In the plane the partition may be arbitrary, while in higher…
Subaddivity type matrix inequalities for concave funcions and symetric norms are given.
We introduce the concept of a standard form for two embedded maximal sphere systems in the doubled handlebody, and we prove an existence and uniqueness result. In particular, we show that pairs of maximal sphere systems in the doubled…
We present a characterization, in terms of projective biduality, for the hypersurfaces appearing in the boundary of the convex hull of a compact real algebraic variety.
We consider a model of random permutations of the sites of the cubic lattice. Permutations are weighted so that sites are preferably sent onto neighbors. We present numerical evidence for the occurrence of a transition to a phase with…