A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Weak solutions found for Chern-Ricci flow on complex surfaces.
The study examines exceptional sets for radial limits of superharmonic functions on curved manifolds.
Minimal surfaces in spheres are classified based on a Ricci-like condition.
Elliptic curves and braid groups linked through configuration spaces.
For the purposes of this paper, Dehn surgery along a curve K in a 3-manifold M with slope r is `exceptional' if the resulting 3-manifold M_K(r) is reducible or a solid torus, or the core of the surgery solid torus has finite order in the fundamental group of M_K(r). We show that, providing the exterior of K is irreduci…
Complex projective manifolds without rational curves are quotients of Abelian varieties.
Proves nonnegatively curved hypersurfaces in hyperbolic space are usually properly embedded.
This goal of the paper is to show that the automorphisms of the complex of curves in a surface are induced by the self-homeomorphisms of the surface except the surface is the 2-holed torus.
We study a class of exceptional minimal surfaces in spheres for which all Hopf differentials are holomorphic. Extending results of Eschenburg and Tribuzy \cite{ET0}, we obtain a description of exceptional surfaces in terms of a set of absolute value type functions, the -invariants, that determine the geometry of the…
We give an algebraic way of distinguishing the components of the exceptional strata of quadratic differentials in genus three and four. The complete list of these strata is (9, -1), (6,3,-1), (3,3,3, -1) in genus three and (12), (9,3), (6,6), (6,3,3) and (3,3,3,3) in genus four. This result is part of a more general in…
In this survey paper we give a proof of hyperbolicity of the complex of curves for a non-exceptional surface S of finite type combining ideas of Masur/Minsky and Bowditch. We also shortly discuss the relation between the geometry of the complex of curves and the geometry of Teichmueller space.
The paper studies hyperbolic phenomena on closed surfaces using bicorn curves.
We classify curves in the moduli space of curves that are both Shimura- and Teichmueller curves: Except for the moduli space of genus one curves there is only a single such curve. We start with a Hodge-theoretic description of Shimura curves and of Teichmueller curves that reveals similarities and differences of the tw…
Study of spatial curves in generalized Minkowski spaces.
New method identifies vanishing arcs for curve singularities.
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve has attracted much interest. In the present paper, we propose a new method to construct a surface interpolating a given curve as the asymptotic curve of it. Also, we analyze the co…
We prove an equidistribution result for totally geodesic submanifolds in a compact locally symmetric space. In the case of Hermitian locally symmetric spaces, this gives a convergence theorem for currents of integration along totally geodesic subvarieties. As a corollary, we obtain that on a complex surface which is a …
We give a combinatorial proof of an unpublished result of E. Klarreich: The Gromov boundary of the complex of curves of a non-exceptional oriented surface S of finite type can naturally be identified with the space of minimal geodesic laminations on S which fill up S, equipped with a coarse Hausdorff topology.
Geometry of holomorphic curves from point of view of open Toda systems is discussed. Parametrization of curves related this way to non-exceptional simple Lie algebras is given. This gives rise to explicit formulas for minimal surfaces in real, complex and quaternionic projective spaces or complex quadrics. The paper ge…
In this note, we develop a condition on a closed curve on a surface or in a 3-manifold that implies that the curve has the property that its length function on the space of all hyperbolic structures on the surface or 3-manifold completely determines the curve. For an orientable surface of negative Euler characteris…
The paper proves a slope equality for smooth plane curve fibrations and applies it to Durfee's conjecture.
Cayley's (ruled cubic) surface carries a three-parameter family of twisted cubics. We describe the contact of higher order and the dual contact of higher order for these curves and show that there are three exceptional cases.
We investigate the case of the Kahler-Ricci flow blowing down disjoint exceptional divisors with normal bundle O(-k) to orbifold points. We prove smooth convergence outside the exceptional divisors and global Gromov-Hausdorff convergence. In addition, we establish the result that the Gromov-Hausdorff limit coincides wi…
Five types of translation surfaces with constant curvature found in Galilean 3-space.
These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and stacks) important in the study of moduli spaces of curves and abelian varieties thro…
The study characterizes a complex curve of residueless meromorphic differentials on elliptic curves.
Smooth compactness theorem for elasticae, except straight segments.
The paper extends a geometric model using singular curves.
Classifies manifolds with quasipositive curvature.
We give a one parameter family of exceptional planar 5-webs. Each web is formed by four pencils of lines and by a foliation defined by the level curves of a function sn_k(x)sn_k(y) where sn_k denotes a Jacobi's elliptic function.
Proves a theorem for Assouad dimension with applications to distance sets and radial projections.
Establishes a Li-Yau type inequality for curves in any codimension.
Defines Lewy curves in para-CR geometry and characterizes their path geometries.
We prove that there are no pseudoholomorphic theories of anything other than curves, even if one allows more general spaces than almost complex manifolds. The proof is elementary, except for theories of pseudoholomorphic hypersurfaces, where topological techniques are needed. Surprisingly, hypersurface theories exist `…
The curvature of web curves is studied in 3D manifolds.
This research classifies Teichmüller curves in genus 2, proving parity conjectures for specific cases.
Study on Coxeter groups' boundary planarity, finding exceptions.
The study examines metrics on Riemann moduli spaces and their asymptotic expansions.
Study of generalized Bishop frames on curves in 4D space.
These are notes of lectures given at the NATO Summer School, Montreal 1995. Taubes's recent spectacular work setting up a correspondence between -holomorphic curves in symplectic 4-manifolds and solutions of the Seiberg-Witten equations counts -holomorphic curves in a somewhat new way. The "standard" theory conce…
Word length in surface groups linked to intersection numbers.
We prove the "End Curve Theorem," which states that a normal surface singularity with rational homology sphere link is a splice-quotient singularity if and only if it has an end curve function for each leaf of a good resolution tree. An "end-curve function" is an analytic function $(X,o)\to (\C,0)$ whose ze…
Paper constructs Kuranishi charts for symplectic manifold moduli spaces.
The paper resolves fundamental groups for three exceptional surface singularity families.
This article is about the graph genus of certain well studied graphs in surface theory: the curve, pants and flip graphs. We study both the genus of these graphs and the genus of their quotients by the mapping class group. The full graphs, except for in some low complexity cases, all have infinite genus. The curve grap…
Free finite group actions on non-positively curved 3-manifolds
We prove that every topological conjugation between two germs of singular holomorphic curves in the complex plane is homotopic to another conjugation which extends homeomorphically to the exceptional divisors of their minimal desingularizations. As an application we give an explicit presentation of a finite index subgr…
Develops a simple model to understand learning curves for arbitrary power laws.