5 papers
The Four Periodic Inscription Problem
Ali Naseri Sadr
We prove that four periodic curves in inscribe a family of isosceles trapezoids for every angle , whose similarity types are determined by the signed areas…
Inscriptions in non-Euclidean Geometries
Ali Naseri Sadr
We show how inscription problems in the plane can be generalized to Riemannian surfaces of constant curvature. We then use ideas from symplectic and Riemannian geometry to prove th…
Periodic Inscription of Isosceles Trapezoids
Ali Naseri Sadr
We prove that a pair of continuous disjoint periodic curves in inscribes an isosceles trapezoid with any similarity type. The case of smooth curves can be identified w…
A Table Theorem for Surfaces with Odd Euler Characteristic
Ali Naseri Sadr
We use the square peg problem for smooth curves to prove a generalized table Theorem for real valued functions on Riemannian surfaces with odd Euler characteristic. We then use thi…
Classification of Lattices Bounded by Large Surgeries of Knots
Ali Naseri Sadr
We classify all the lattices realized as the intersection form of a positive definite four manifold with boundary for a knot in the three sphere and a positive integ…