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We establish an area-type formula for the intrinsic spherical Hausdorff measure of every regular curve embedded in an arbitrary graded group.
Lifting Tropical Curves in Space and Linear Systems on Graphs
Tropical Curves in Space Linear Systems Graphs
2010/12/2
Tropicalization is a procedure for associating a polyhedral complex to a subva-riety of an algebraic torus. We study the question on which graphs arise from tropicalizing algebraic curves. By using Ba...
DESCENDENT INTEGRALS AND TAUTOLOGICAL RINGS OF MODULI SPACES OF CURVES
DESCENDENT INTEGRALS TAUTOLOGICAL RINGS MODULI SPACES CURVES
2018/4/19
The main objective of this paper is to give a summary of our recent work on recursion formulae for intersection numbers on moduli spaces of curves and their applications.We also present a conjectural ...
We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimens...
Virtual neighborhoods and pseudo-holomorphic curves
pseudo-holomorphic curves Virtual neighborhoods
2010/3/3
Virtual neighborhoods and pseudo-holomorphic curves。
For any d\ge 5, I constructed infinitely many pairwise smoothly non-equivalent surfaces F\subset\Cp{2} homeomorphic to a non-singular algebraic curve of degree d, realizing the same homology class as ...
Combinatorial patchworking of real pseudo-holomorphic curves
real pseudo-holomorphic curves algebraic curves
2010/3/1
The Viro method of construction of real algebraic varieties with prescribed topology uses convex subdivisions of Newton polyhedra. We show that in the case of arbitrary (not necessarily convex) subdiv...
On Pseudohyperbolical Curves in Minkowski Space-Time
Minkowski space--time pseudohyperbolic space curvature
2010/3/1
In this paper, we characterize all spacelike, timelike and null curves lying on the pseudohyperbolic space H03 in the Minkowski space--time E14. Moreover, we prove that there are no timelike and no nu...
Topology Determination and Isolation for Implicit Plane Curves
Plane curve topology isolating box certied meshing interval analysis
2013/9/9
A method is proposed to generate an isolation for a plane curve, which is a set of boxes covering the curve, having the same topology as the curve, and approximating the curve to any given precision. ...
Hyperbolic mean curvature flow: Evolution of plane curves
hyperbolic mean curvature °ow hyperbolic Monge-Ampμere equa- tion closed plane curve short-time existence
2018/4/20
In this paper we investigate the one-dimensional hyperbolic mean curvature °ow for closed plane curves. More precisely, we consider a family of closed curves F : S1 ￡[0; T) ! R2 which satisˉes the fol...
Classification and generation of 3D discrete curves
3D Discrete curves chain coding curve classification
2010/9/16
We present a quantitative approach to the representation, classification,and generation of families of 3D (three-dimensional) particular discrete closed curves. Any 3D continuous curve can be digitali...
Approximation of curves by fairness cubic splines
Smoothness Variational curve Fairness spline Cubic spline
2010/9/15
In this paper we present an approximation method of curves by a new type of spline functions called fairness cubic splines from a given Lagrangian data set under fairness constraints. An approximating...
In this paper, we give an elementary proof of the fact that symmetric arithmetically Cohen-Macaulay monomial curves are set-theoretic complete intersections. The proof is constructive and provides the...
<正> INTRODUGTION.1.In the proiective theory of a curve in ordinary space thereare introduced various systems of tetrahedrons associated to a pointof the curve.Most of them are,more or less,artificial ...
<正> In a recent paper of the same title we studied the plane sectionsof the circumscribed developable of a curve in the projective n-dimen-sional space Sn(n(?)3) confining ourselves to the considerati...