Related papers: Random Surfaces with Boundary
Granular fronts are a common yet unexplained phenomenon emerging during the gravity driven free-surface flow of concentrated suspensions. They are usually believed to be the result of fluid convection in combination with particle size…
Granular surfaces tend to develop lateral ripples under the action of surface forces exerted by rolling wheels, an effect known as washboard or corrugated road. We report the results of both laboratory experiments and soft-particle direct…
The ruled surfaces, i.e., surfaces generated by one parametric set of lines, are widely used in the~field of applied geometry. An~isophote on a surface is a curve consisting of surface points whose normals form a constant angle with some…
This paper completes the foundations of neatly integrable normal distribution theory on manifolds with boundary. Normal distributions are those which contain vectors transverse to the boundary along its entirety. The theory is observed to…
Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This…
Using a microscopic phase-space model of the membrane system, the boundary condition at a membrane is derived. According to the condition, the substance flow across the membrane is proportional to the difference of the substance…
In the paper "Isoperimetry of waists and local versus global asymptotic convex geometries", it was proved that the existence of nicely bounded sections of two symmetric convex bodies K and L implies that the intersection of randomly rotated…
One can embed arbitrarily many disjoint, non-parallel, non-boundary parallel, incompressible surfaces in any three manifold with at least one boundary component of genus two or greater [4]. This paper proves the contrasting, but not…
We study the regularity properties of random wavelet series constructed by multiplying the coefficients of a deterministic wavelet series with unbounded I.I.D. random variables. In particular, we show that, at the opposite to what happens…
We introduce and study a novel semi-random multigraph process, described as follows. The process starts with an empty graph on $n$ vertices. In every round of the process, one vertex $v$ of the graph is picked uniformly at random and…
For each integer $g\geq 1$ we use variational methods to construct in the unit $3$-ball $B$ a free boundary minimal surface $\Sigma_g$ of symmetry group $\mathbb{D}_{g+1}$. For $g$ large, $\Sigma_g$ has three boundary components and genus…
We consider a one dimensional random-walk-like process, whose steps are centered Gaussians with variances which are determined according to the sequence of arrivals of a Poisson process on the line. This process is decorated by independent…
The problem of a bouncing ball on a non-planar surface is investigated. We discovered that surface undulation adds a horizontal component to the impact force, which acquires a random character. Some aspects of Brownian motion are found in…
We show that all hyperbolic surfaces admit an ideal triangulation with bounded shear parameters. This upper bound depends logarithmically on the topology of the surface.
Given a Riemann surface and a riemannian manifold M with certain restrictions, we construct a cobordism invariant of M. This invariant is a generalization of the elliptic genus and it shares some similar properties.
Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic…
Coincidences of maps between smooth manifolds are studied via a geometric approach which involves (nonstabilized) normal bordism theory and pathspaces.
Let $A$ be a compact $d$-dimensional $C^2$ Riemannian manifold with boundary, embedded in ${\bf R}^m$ where $m \geq d \geq 2$, and let $B$ be a nice subset of $A$ (possibly $B=A$). Let $X_1,X_2, \ldots $ be independent random uniform points…
The deviation of a general convex body with twice differentiable boundary and an arbitrarily positioned polytope with a given number of vertices is studied. The paper considers the case where the deviation is measured in terms of the…
Suppose an interval is put on a horizontal line with random roughness. With probability one it is supported at two points, one from the left, and another from the right from its center. We compute probability distribution of support points…