Related papers: On the structure of foliations on dilation surface…
In this paper, we present numerical and experimental evidence of directional wave behavior, i.e. beaming and diffraction, along high-order rotational symmetries of quasicrystalline elastic metamaterial plates. These structures are obtained…
In this paper we deal with the global properties of Willmore surfaces in spheres via the harmonic conformal Gauss map using loop groups. We first derive a global description of those harmonic maps which can be realized as conformal Gauss…
There is a deformation of the ordinary differential calculus which leads from the continuum to a lattice (and induces a corresponding deformation of physical theories). We recall some of its features and relate it to a general framework of…
We develop a dynamical density functional theory based model for the drying of colloidal films on planar surfaces. We consider mixtures of two different sizes of hard-sphere colloids. Depending on the solvent evaporation rate and the…
A classical result of Bondal-Orlov states that a standard flip in birational geometry gives rise to a fully faithful functor between derived categories of coherent sheaves. We complete their embedding into a semiorthogonal decomposition by…
Thin surfaces are ubiquitous in nature, from leaves to cell membranes, and in technology, from paper to corrugated containers. Structural thinness imbues them with flexibility, the ability to easily bend under light loads, even as their…
We prove that for any two Riemannian metrics $\sigma_1, \sigma_2$ on the unit disk, a homeomorphism $\partial\mathbb{D}\to\partial\mathbb{D}$ extends to at most one quasiconformal minimal diffeomorphism $(\mathbb{D},\sigma_1)\to…
In this paper, we prove that any K\"ahler Ricci shrinker surface has bounded sectional curvature. Combining this estimate with earlier work by many authors, we provide a complete classification of all K\"ahler Ricci shrinker surfaces.
{\it Surface-directed spinodal decomposition} (SDSD) is the kinetic interplay of phase separation and wetting at a surface. This process is of great scientific and technological importance. In this paper, we report results from a numerical…
We study the deformation theory of rational curves on primitive symplectic varieties and show that if the rational curves cover a divisor, then, as in the smooth case, they deform along their Hodge locus in the universal locally trivial…
Using the fractional discrete Laplace operator for triangle meshes, we introduce a fractional combinatorial Calabi flow for discrete conformal structures on surfaces, which unifies and generalizes Chow-Luo's combinatorial Ricci flow for…
Tearing a thin sheet by forcing a rigid object through it leads to complex crack morphologies; a single oscillatory crack arises when a tool is driven laterally through a brittle sheet, while two diverging cracks and a series of…
We consider any Finsler metric on a closed, orientable surface of genus greater than one. H. M. Morse proved that we can associate an asymptotic direction to minimal rays in the universal cover (in the Poincar\'e disc: a point on the unit…
We prove a "gluing" theorem for monotone homotopies; a monotone homotopy is a homotopy through simple contractible closed curves which themselves are pairwise disjoint. We show that two monotone homotopies which have appropriate overlap can…
Based on density-functional theory we analyze the full phase diagram, the occurrence of long-ranged orientational order, and the structural properties of dipolar fluids. As a model system we consider the Stockmayer fluid that consists of…
Nivat's conjecture is a famous open problem in symbolic dynamics. The existence of nonexpansive lines that when endowed with a given orientation are one-sided nonexpansive directions is at the heart of some advances. In his Ph.D. thesis,…
Mitsumatsu constructed leafwise symplectic structures of certain codimension one foliations of the 5-sphere. This inspired the present author to improve his result on convergence of contact structure to foliation. We describe convergence of…
Let $S$ be a compact complex surface in class VII$_0^+$ containing a cycle of rational curves $C=\sum D_j$. Let $D=C+A$ be the maximal connected divisor containing $C$. If there is another connected component of curves $C'$ then $C'$ is a…
In the companion paper arXiv:2110.05298, we developed the deformation theory of symplectic foliations, focusing on geometric aspects. Here, we address some algebraic questions that arose naturally. We show that the $L_{\infty}$-algebra…
We construct harmonic diffeomorphisms from the complex plane $C$ onto any Hadamard surface $M$ whose curvature is bounded above by a negative constant. For that, we prove a Jenkins-Serrin type theorem for minimal graphs in $M\times R$ over…