WEEKLY ACTIVITIES

Time: 14h00, Thursday, May 5, 2016
Location: Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: We present some analysis and geometric properties of shortest paths between two points in Euclidean spaces E. Given two points $a, b \in E$ and a sequence of line segments $e_1, . . . , e_k$ in $E$, a path that joins a to b and goes through $e_1, . . . , e_k$ in that order is called an ordered path. An ordered path that is shortest is called a shortest ordered path. We discuss the existence and uniqueness of shortest ordered paths and conditions for concatenation of two shortest ordered paths to be a shortest ordered path. We then focus on shortest paths between two points on polygons, sequences of adjacent triangles in 2 and 3 dimensional spaces, respectively, especially on straightest paths on the sequences of adjacent triangles.
(joint work with Nguyễn Ngọc Hải and Phan Thành An)