4 papers
math.DG2025
A note on the possibility of a motion without crossing a given subset
Reza Mirzaie
We study the fractal dimension of a given subset X of R^{n} such that a motion is possible without crossing X.
math.DG2025
On topology estimation of submanifolds in Riemannian manifolds by random points
Reza Mirzaie
We show that, by sampling a sufficiently large number of random points in a neighborhood of a compact submanifold M of a Riemannian manifold N, one can recover the topology of M wi…
math.DG2025
How many points in a point cloud is sufficient for accurate estimation of the curvature
R. Mirzaie
We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or sur…
math.DG2025
A remark on the reach and upper bounds on some extrinsic geometry invariants of submanifolds
Reza Mirzaie
We consider a compact submanifold of a Riemannian manifold and we use the second variation formula as a tool to drive some geometric results on reach the reach of $…