https://neckpinch.com/authors/matei-p-coiculescu/New arXiv papers by Matei P. Coiculescu, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2106.09213/arxiv:2106.09213Thu, 17 Jun 2021 00:00:00 GMTMatei P. Coiculescu, Richard Evan Schwartz — We consider the curve shortening flow applied to a class of figure-eight curves: those with dihedral symmetry, convex lobes, and a monotonicity assumption on the curvature. We prove that when (non-conformal) linear transformations are applied to the solution so as to keep the bounding box the unit square, the renormalized limit converges to a quadrilateral which we call a bowtie. Along the way we prove that suitably chosen arcs of our evolving curves, when suitably rescaled, converge to the Grim Reaper Soliton under the flow. Our Grim Reaper Theorem is an analogue of a theorem of S. Angenent, which is proven in the locally convex case.Curve shorteningSelf-shrinkers & translators https://neckpinch.com/papers/2103.15594/arxiv:2103.15594Thu, 25 Mar 2021 00:00:00 GMTMatei P. Coiculescu — This thesis presents three results in geometric analysis. We first analyze the curve-shortening flow on figure eight curves in the plane. Afterwards, we examine the point-wise curvature preserving flow on space curves. Lastly, we present an abridgment of our work on a family of three-dimensional Lie groups, which, when equipped with canonical left-invariant metrics, interpolate between Sol and hyperbolic space.Curve shortening3-manifoldsHomogeneous spaces