Related papers: Existence of optimal flat ribbons
In this paper we study infinitesimal and finite flexibility for generic semidiscrete surfaces. We prove that generic 2-ribbon semidiscrete surfaces have one degree of infinitesimal and finite flexibility. In particular we write down a…
We consider minimization problems in the calculus of variations set in a sequence of domains the size of which tends to infinity in certain directions and such that the data only depend on the coordinates in the directions that remain…
We prove two results about transforming any convex polyhedron, modeled as a linkage L of its edges. First, if we subdivide each edge of L in half, then L can be continuously flattened into a plane. Second, if L is equilateral and we again…
Given interpolation points $P_1,P_2,\ldots,P_n$ in the plane, it is known that there does not exist an interpolating curve with minimal bending energy, unless the given points lie sequentially along a line. We say than an interpolating…
We employ equivariant variational methods to construct new examples of nonplanar free boundary minimal discs in ellipsoids. We also prove that every ellipsoid contains at least three distinct embedded free boundary minimal annuli with…
We give a criterion when a planar tree-like curve, i.e. a generic immersed plane curve each double point of which cuts it into two disjoint parts, can be send by a diffeomorphism of the plane onto a curve with no inflection points. We also…
Nontrivial infinitesimal bendings for a class of two-dimensional surfaces are constructed. The surfaces considered here are orientable; compact; with boundary; have positive curvature everywhere except at finitely many planar points; and…
We show that for a complete Ricci shrinker there exists a sequence of points tending to infinity whose norms of the Ricci tensor grow at most linearly.
We establish local existence and a quasi-optimal error estimate for piecewise cubic minimizers to the bending energy under a discretized inextensibility constraint. In previous research a discretization is used where the inextensibility…
We consider the problem of an optimal distribution of soft and hard material for nonlinearly elastic planar beams. We prove that under gravitational force the optimal distribution involves no microstructure and is ordered, and we provide…
We look for minimizers of the buckling load problem with perimeter constraint in any dimension. In dimension 2, we show that the minimizing plates are convex; in higher dimension, by passing through a weaker formulation of the problem, we…
In this paper we characterize the extremal points of the unit ball of the Benamou--Brenier energy and of a coercive generalization of it, both subjected to the homogeneous continuity equation constraint. We prove that extremal points…
We investigate the spectrum of the Dirichlet Laplacian in a unbounded strip subject to a new deformation of "shearing": the strip is built by translating a segment oriented in a constant direction along an unbounded curve in the plane. We…
In this article, we investigate the possible torsion subgroups of twists of abelian varieties with good reduction. As an application, we prove a theorem concerning ramified primes over any quadratic extension where odd-order torsion growth…
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…
In this paper we study the existence and the dynamics of a very special class of motions, which satisfy a strong global minimization property. More precisely, we call a free time minimizer a curve which satisfies the least action principle…
We show that for any family of curves over a base scheme of finite type over the prime field $\mathbb F_p$ such that the monodromy is ``maximal'', there exist infinitely many closed points of the base scheme such that the Jacobian of fibre…
To formulate our results let $f$ be a continuous map from $\mathbb R^n$ to $2^{\mathbb R^n}$ and $k$ a natural number such that $|f(x)|\leq k$ for all $x$. We prove that $f$ is fixed-point free if and only if its continuous extension…
We consider periodic and quasi-periodic solutions of the three-body problem with homogeneous potential from the point of view of the equivariant calculus of variations. First, we show that symmetry groups of the Lagrangian action functional…
We propose a model for nonlinearly elastic membranes undergoing finite deformations while confined to a regular frictionless surface in $\mathbb{R}^3$. This is a physically correct model of the analogy sometimes given to motivate harmonic…