Related papers: A local description of 2-dimensional almost minima…
We study the interaction of an incompressible fluid in two dimensions with an elastic structure yielding the moving boundary of the physical domain. The displacement of the structure is described by a linear viscoelastic beam equation. Our…
We relate generalized Lebesgue decompositions of measures in terms of curve fragments (Alberti representations) and Weaver derivations. This correspondence leads to a geometric characterization of the local norm on the Weaver cotangent…
We establish sufficient conditions for existence of curves minimizing length as measured with respect to a degenerate metric on the plane while enclosing a specified amount of Euclidean area. Non-existence of minimizers can occur and…
In this article we prove that the union of two almost orthogonal planes in R4 is Almgren-minimal. This gives an example of a one parameter family of minimal cones, which is a phenomenon that does not exist in R3. This work is motivated by…
Inspired by the log Gromov-Witten (or GW) theory of Gross-Siebert/Abramovich-Chen, we introduce a geometric notion of log J-holomorphic curve relative to a simple normal crossings symplectic divisor defined in [FMZ1]. Every such moduli…
We analyze the asymptotic behavior of a $2$-dimensional integral current which is almost minimizing in a suitable sense at a singular point. Our analysis is the second half of an argument which shows the discreteness of the singular set for…
In the presence of a positive, compactly supported measure on an affine algebraic curve, we relate the density of polynomials in Lebesgue $L^2$-space to the existence of analytic bounded point evaluations. Analogues to the complex plane…
The main purpose of this paper is to explore the structure of local and regular Dirichlet forms associated with symmetric linear diffusions. Let $(\mathcal{E},\mathcal{F})$ be a regular and local Dirichlet form on $L^2(I,m)$, where $I$ is…
We prove various representations and density results for Hardy spaces of holomorphic functions for two classes of bounded domains in $\mathbb C^n$, whose boundaries satisfy minimal regularity conditions (namely the classes $C^2$ and…
We follow the diffusive motion of colloidal particles of diameter $d$ in soap films of varying thickness $h$ with fluorescence microscopy. Diffusion constants are obtained both from one- and two-particle microrheological measurements of…
We classify cylindrical surfaces in the Euclidean space whose mean curvature is a $n$th-power of the distance to a reference plane. The generating curves of these surfaces, called $n$-elastic curves, have a variational characterization as…
In this paper we compute the Hausdorff distance between sets of continuous curves and sets of piecewise constant or linear discretizations. These sets are Sobolev balls given by the continuous or discrete $L^p$-norm of the derivatives. We…
We propose a fast method to determine the local curvature in two-dimensional (2D) systems with arbitrary shape. The curvature information, combined with elastic constants obtained for a planar system, provides an accurate estimate of the…
We show that in any $d$-dimensional real normed space, unit balls can be packed with density at least \[\frac{(1-o(1))d\log d}{2^{d+1}},\] improving a result of Schmidt from 1958 by a logarithmic factor and generalizing the recent result of…
Let $D$ be a bounded domain in $\mathbf C^2$ with a non-compact group of holomorphic automorphisms. Model domains for $D$ are obtained under the hypothesis that at least one orbit accumulates at a boundary point near which the boundary is…
We study some special almost complex structures on strictly pseudoconvex domains. They appear naturally as limits under a nonisotroping scaling procedure and play a role of model objects in the geometry of almost complex manifolds with…
Following Katz-Sarnak, Iwaniec-Luo-Sarnak, and Rubinstein, we use the 1- and 2-level densities to study the distribution of low lying zeros for one-parameter rational families of elliptic curves over Q(t). Modulo standard conjectures, for…
We show that if $E \i \R^n$ is a Reifenberg flat set $E$ of dimension $d$ at scale $r_0$, we can find a smooth surface $\Sigma_0$ of dimension $d$ which is close to $E$ at the scale $r_0$. When $E$ is a Reifenberg flat set, this allows us…
Consider a random set of points on the unit sphere in $\mathbb{R}^d$, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the…
We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general…