Convexity of Nilpotent Balls
نویسنده
چکیده
We consider the shape of balls for nilpotent Lie groups endowed with a left invariant Riemannian or sub-Riemannian metric. We prove that when the algebra is graded these balls are homeomorphic to the standard Euclidean ball. For two-step nilpotent groups we show that the intersections of the ball with the central cosets are star-shaped, and in special cases convex.
منابع مشابه
Local Convexity Properties of Balls in Apollonian and Seittenranta’s Metrics
We consider local convexity properties of balls in the Apollonian and Seittenranta’s metrics. Balls in the Apollonian metric are considered in the twice punctured space and starlike domains. Balls in Seittenranta’s metric are considered in the twice punctured space and in the punctured ball.
متن کاملLOCAL CONVEXITY PROPERTIES OF j-METRIC BALLS
This paper deals with local convexity properties of the j-metric. We consider convexity and starlikeness of the j-metric balls in convex, starlike and general subdomains of R.
متن کاملAround heat decay on forms and relations of nilpotent Lie groups
One knows that the large time heat decay exponent on a nilpotent group is given by half the growing rate of the volume of its large balls. This work deals with the similar problem of trying to interpret geometrically the heat decay on (1-)forms. We will show how it is (partially) related to the depth of the relations required to define the group.
متن کاملOptimal Covering of a Straight Line Applied to Discrete Convexity
The relation between a straight line and its digitization as a digital straight line is often expressed using a notion of proximity. In this contribution, we consider the covering of the straight line by a set of balls centered on the digital straight line pixels. We prove that the optimal radius of the balls is strictly less than one, and can be expressed as a function of the slope of the stra...
متن کاملOn local convexity in graphs
A set K of nodes of a graph G is geodesically convex (respectively, monophonically convex) if K contains every node on every shortest (respectively, chordless) path joining nodes in K. We investigate the classes of graphs which are characterized by certain local convexity conditions with respect to geodesic convexity, in particular, those graphs in which balls around nodes are convex, and those...
متن کامل