One property of a planar curve whose convex hull covers a given convex figure

平面布朗运动与桥的星形包的期望面积

Expected area of the star hull of planar Brownian motion and bridge

研究平面布朗运动与桥的星形包，证明其期望面积分别为3π/8和π/4，通过分析半直线首达时与位置的联合分布得到简洁的拉普拉斯变换。

平面布朗运动退出单位盘时凸包的期望周长

Expected perimeter and area of the convex hull of planar Brownian motion stopped upon exiting the unit disk

研究平面布朗运动在退出单位盘时凸包的周长期望，通过计算最大水平位移的期望值，利用截断盘的调和测度得出精确表达式，并讨论凸包面积期望的非平凡界及计算难度。

平面布朗运动凸包的内切半径与逆内切半径过程的改进界

Improved bounds on the inradius and inverse inradius process of the convex hull of planar Brownian motion

本文针对平面布朗运动凸包的内切半径与逆内切半径，通过推导一维布朗运动极差期望闭式、沙漏域首出时间矩，改进了其期望与方差的界。

双曲三维空间中的凸包体积

Convex Hull Volumes in Hyperbolic 3-Space

研究双曲三维空间中闭集的几何条件，证明其凸包体积无限，回答Danny Calegari问题，并刻画平面自相似集的几何特性。

The middle hedgehog of a planar convex body

A convexity point of a convex body is a point with the property that the union of the body and its reflection in the point is convex. It is proved that in the plane a typical convex body (in the sense of Baire category) has infinitely many convexity points. The proof makes use of the `middle hedgehog' of a planar convex body $K$, which is the curve formed by the midpoints of all affine diameters of $K$. The stated result follows from the fact that for a typical planar convex body the convex hull of the middle hedgehog has infinitely many exposed points.

Aperture-Angle and Hausdorff-Approximation of Convex Figures

The aperture angle alpha(x, Q) of a point x not in Q in the plane with respect to a convex polygon Q is the angle of the smallest cone with apex x that contains Q. The aperture angle approximation error of a compact convex set C in the plane with respect to an inscribed convex polygon Q of C is the minimum aperture angle of any x in C Q with respect to Q. We show that for any compact convex set C in the plane and any k > 2, there is an inscribed convex k-gon Q of C with aperture angle approximation error (1 - 2/(k+1)) pi. This bound is optimal, and settles a conjecture by Fekete from the early…