Christine Breiner
Johns Hopkins University
Department of Mathematics
105 Krieger Hall
3400 N. Charles Street
Baltimore, MD 21218
Office: 105 Krieger Hall
Email: cbreiner"at"math"dot"jhu"dot"edu
Research
I am interested in the geometry of complete, properly embedded
minimal surfaces in Euclidean space. While complete, properly embedded
minimal disks have been fully classified (in R^3 the only two surfaces are the
helicoid and the plane), I am presently interested in complete, properly
embedded minimal surfaces of finite genus and one end. Currently, a major
question that remains unanswered is whether or not the embedded genus-one
helicoid is unique.
Advisor: Bill Minicozzi
Publications
Helicoid-Like Minimal Disks and Uniqueness.
Joint with Jacob Bernstein. Preprint.
arxiv link
Abstract: We show that an embedded minimal disk in R^3 with large curvature is bi-Lipschitz with a piece of a helicoid. Additionally, a simplified proof of the uniqueness of the helicoid is provided.
Distortions of the Helicoid. Joint with Jacob Bernstein. Preprint. arxiv link
Abstract: Colding and Minicozzi have shown that an embedded minimal disk $0\in\Sigma\subset B_R$ in $\Real^3$ with large curvature at $0$ looks like a helicoid on the scale of $R$. Near $0$, this can be sharpened: on the scale of $|A|^{-1}(0)$, $\Sigma$ is close, in a Lipschitz sense, to a piece of a helicoid. We use surfaces constructed by Colding and Minicozzi to see this description cannot hold on the scale $R$.
Teaching
Intro to Calculus - Fall 2005 (Taught course)
Calculus I - Fall 2004, Spring 2005
Calculus II - Spring 2007, Spring 2008
Calculus III - Spring 2006, Fall 2006
Analysis and Honors Analysis - Fall 2007