Mathematical Sciences: Geometric Analysis: Research and Conformal Mapping, Extremal Length, and Riemann Surfaces

伯顿罗丹将继续调查一个新的 黎曼映射定理的计算方法。 这是因为发现了共形 映射和圆填充。这种调查应导致 对这两个领域的新见解和新技术的数值 保角映射此外，还将开展研究， 几何函数理论的其他领域。 这项研究将涉及以下调查 区域：边界行为与 黎曼映射函数和区域几何; 布朗漂移定律在共形性研究中的应用 映射;全纯与拟共形黎曼族 映射函数;调和测度估计;共形 曲线多边形映射;极值长度与调和 衡量关系。

Burton Rodin will continue investigations into a newly developed computational approach to the Riemann mapping theorem. This follows from the discovery of connections between conformal mapping and circle packing. Such investigations should lead to new insights into both areas and to new techniques in numerical conformal mapping. In addition research will be carried out into other areas of geometric function theory. This research will involve investigations into the following areas: the relationship between the boundary behavior of the Riemann mapping function and the geometry of the region; the application of Brownian excursion laws in the study of conformal mapping; holomorphic and quasiconformal families of Riemann mapping functions; harmonic measure estimates; the conformal mapping of curvilinear polygons; extremal length and harmonic measure relationships.