5 papers
The Tight Spanning Ratio of the Rectangle Delaunay Triangulation
Andrè van Renssen, Yuan Sha, Yucheng Sun +1
Spanner construction is a well-studied problem and Delaunay triangulations are among the most popular spanners. Tight bounds are known if the Delaunay triangulation is constructed…
Min-max free boundary minimal surface with genus at least one
Yuchin Sun
In this paper, we build up a min-max theory for minimal surfaces using sweepouts of surfaces of genus and ideal boundary components. We show that the width for…
Morse Index Bound for Minimal Torus
Yuchin Sun
The min-max construction of minimal spheres using harmonic replacement is introduced by Colding and Minicozzi and generalized by Zhou to conformal harmonic torus. We prove that the…
Morse Index Bound for Minimal Two Spheres
Yuchin Sun
Given a closed manifold of dimension at least three, with non trivial homotopy group π_3(M) and a generic metric, we prove that there is a finite collection of harmonic spheres wit…
Some variants of Lagrange's four squares theorem
Yu-Chen Sun, Zhi-Wei Sun
Lagrange's four squares theorem is a classical theorem in number theory. Recently, Z.-W. Sun found that it can be further refined in various ways. In this paper we study some conje…