Related papers: Formal conserved quantities for isothermic surface…
We study entanglement spectra of gapped states on the surfaces of symmetry-protected topological phases. These surface states carry anomalies that do not allow them to be terminated by a trivial state. Their entanglement spectra are…
A new class of examples of surfaces with maximal Picard number is constructed. These carry pencils of genus two or three curves such their Jacobian fibrations are isogenous to fibre products of elliptic modular surfaces.
We present a definition of discrete channel surfaces in Lie sphere geometry, which reflects several properties for smooth channel surfaces. Various sets of data, defined at vertices, on edges or on faces, are associated with a discrete…
We characterize helix surfaces (constant angle surfaces) in the special linear group $\mathrm{SL}(2,\r)$. In particular, we give an explicit local description of these surfaces in terms of a suitable curve and a 1-parameter family of…
Let $(\Sigma,p)$ be a pointed Riemann surface of genus $g\geq 1$. For any integer $k\geq 1$, we parametrize the space of meromorphic quadratic differentials on $\Sigma$ with a pole of order $(k+2)$ at $p$, having a connected critical graph…
Let S be an immersed horizontal surface in a 3-dimensional graph manifold. We show that the fundamental group of the surface S is quadratically distorted whenever the surface is virtually embedded (i.e., separable) and is exponentially…
In this paper, we prove a similar result to the fundamental theorem of regular surfaces in classical differential geometry, which extends the classical theorem to the entire class of singular surfaces in Euclidean 3-space known as frontals.…
We give an elaborated treatment of discrete isothermic surfaces and their analogs in different geometries (projective, M\"obius, Laguerre, Lie). We find the core of the theory to be a novel projective characterization of discrete isothermic…
It is well known that in some cases the spectral parameter has a group interpretation. We discuss in detail the case of Gauss-Codazzi equations for isothermic surfaces immersed in $E^3$. The algebra of Lie point symmetries is 4-dimensional…
This paper investigates dynamics that persist under isotopy in classes of orientation-preserving homeomorphisms of orientable surfaces. The persistence of periodic points with respect to periodic and strong Nielsen equivalence is studied.…
The interaction of a quantum field with a background containing a Dirac delta function with support on a surface of codimension 1 represents a particular kind of matching conditions on that surface for the field. In this article we show…
Periodic surface homemorphisms (diffeomorphisms) play a significant role in the the Nielsen-Thurston classification of surface homeomorphisms. Periodic surface homeomorphisms can be described (up to conjugacy) by using data sets which are…
We define a laminar branched surface to be a branched surface satisfying the following conditions: (1) Its horizontal boundary is incompressible; (2) there is no monogon; (3) there is no Reeb component; (4) there is no sink disk (after…
We study a family of lattice polarized $K3$ surfaces which is an extension of the family of Kummer surfaces derived from principally polarized Abelian surfaces. Our family has two special properties. First, it is coming from a resolution of…
Most known examples of doubly periodic minimal surfaces in $\mathbb{R}^3$ with parallel ends limit as a foliation of $\mathbb{R}^3$ by horizontal noded planes, with the location of the nodes satisfying a set of balance equations.…
We study the problem posed by F. Burstall of developing a theory of isothermic Euclidean submanifolds of dimension greater than or equal to three. As a natural extension of the definition in the surface case, we call a Euclidean submanifold…
The basic theory on the conformal geometry of timelike surfaces in pseudo-Riemannian space forms is introduced, which is parallel to the classical framework of Burstall etc. for spacelike surfaces. Then we provide a discussion on the…
We give families of knots and links with pairs of Seifert surfaces that are topologically non-isotopic in $D^4$. This generalizes the main example of Hayden-Kim-Miller-Park-Sundberg and the proof is similarly based on the double branched…
In this paper we extend the novel approach to discrete Painlev\'e equations initiated in our previous work [2]. A classification scheme for discrete Painlev\'e equations proposed by Sakai interprets them as birational isomorphisms between…
Superconformal surfaces in Euclidean space are the ones for which the ellipse of curvature at any point is a nondegenerate circle. They can be characterized as the surfaces for which a well-known pointwise inequality relating the intrinsic…