arXiv subjects

Brian Dean

Publications and source records attributed to Brian Dean.

4 recordsLinked to original sources

arXiv2007

Are seven-game baseball playoffs fairer than five-game series when home-field advantage is considered?

Conventional wisdom in baseball circles holds that a seven-game playoff series is fairer than a five-game series. In an earlier paper, E. Lee May, Jr. showed that, treating each game as an independent event, a seven-game series is not significantly fairer. In this paper, we take a different approach, taking home-field advantage into account. That is, we consider a given series to consist of two disjoint sets of independent events--the home games and the road games. We will take the probability of winning a given road game to be different from the probability of winning a given home game. Our analysis again shows that a seven-game series is not significantly fairer.

math.HO↗

arXiv2005

A generalization of Rado's Theorem for almost graphical boundaries

In this paper, we prove a generalization of Rado's Theorem, a fundamental result of minimal surface theory, which says that minimal surfaces over a convex domain with graphical boundaries must be disks which are themselves graphical. We will show that, for a minimal surface of any genus, whose boundary is "almost graphical" in some sense, that the surface must be graphical once we move sufficiently far from the boundary.

math.DG↗

arXiv2004

Embedded minimal disks with prescribed curvature blowup

We construct a sequence of compact embedded minimal disks in a ball in Euclidean 3-space, whose boundaries lie in the boundary of the ball, such that the curvature blows up only at a prescribed discrete (and hence, finite) set of points on the x_3-axis. This extends a result of Colding and Minicozzi, who constructed a sequence for which the curvature blows up only at the center of the ball, and is a partial affirmative answer to the larger question of the existence of a sequence for which the curvature blows up precisely on a prescribed closed set on the x_3-axis.

math.DG↗

arXiv2003

Compact Embedded Minimal Surfaces of Positive Genus Without Area Bounds

Let M be a 3-manifold (possibly with boundary). We show that, for any positive integer g, there exists an open nonempty set of metrics on M for each of which there are stable compact embedded minimal surfaces of genus g with arbitrarily large area. This extends the result of Colding and Minicozzi for g=1.

math.DG↗