Critical points and curvature for embedded polyhedra
نویسندگان
چکیده
منابع مشابه
Monodromy problem for the degenerate critical points
For the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. When the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. In this paper we will consider the polynomial planar vector fields ...
متن کاملCurvature Extrema and Four-vertex Theorems for Polygons and Polyhedra
Discrete analogs of extrema of curvature and generalizations of the four-vertex theorem to the case of polygons and polyhedra are suggested and developed. Several interrelated approaches are considered. For smooth curves and polygonal lines in the plane, a formula relating the number of extrema of curvature to the winding numbers of the curves (polygonal lines) and their caustics is obtained. O...
متن کاملOn integer points in polyhedra
We give an upper bound on the number of vertices of PI, the integer hull of a polyhedron P, in terms of the dimension n of the space, the number m of inequalities required to describe P, and the size ~ of these inequalities. For fixed n the bound is O(mn~n-1). We also describe an algorithm which determines the number of integer points in a polyhedron to within a multiplicative factor of 1 qE in...
متن کاملCounting Lattice Points in Polyhedra
We present Barvinok’s 1994 and 1999 algorithms for counting lattice points in polyhedra. 1. The 1994 algorithm In [2], Barvinok presents an algorithm that, for a fixed dimension d, calculates the number of integer points in a rational polyhedron. It is shown in [6] and [7] that the question can be reduced to counting the number of integer points in a k-dimensional simplex with integer vertices ...
متن کاملTwo-lattice polyhedra: duality and extreme points
Two-lattice polyhedra are a special class of lattice polyhedra that include network 4ow polyhedra, fractional matching polyhedra, matroid intersection polyhedra, the intersection of two polymatroids, etc. In this paper we show that the maximum sum of components of a vector in a 2-lattice polyhedron is equal to the minimum capacity of a cover for the polyhedron. For special classes of 2-lattice ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1967
ISSN: 0022-040X
DOI: 10.4310/jdg/1214428092