On Lower Dimensional Geometric Flows

PI提出研究一维和二维保形几何流及其在图像处理中的应用。这些想法都是原创的。PI和他的合作者已经取得了一些突破性的成果。这些结果为他们通过积分估计研究低维流以及寻求这些几何流在成像过程中的应用奠定了坚实的基础。目前，PI正在一个跨学科领域工作。PI计划明年开设跨学科课程“成像过程中的几何流”。这位PI正在吸引一些本科生参与他的研究。研究方面的训练将对这些年轻人未来的职业生涯产生很大的影响。

The PI proposes to study one and two-dimensional conformal geometric flows and their applications to image processing. The ideas are original. The PI and his collaborates have obtained some breakthrough results. These results establish the solid foundation for their studies of lower dimensional flows via integral estimates and for them to seek the applications of these geometric flows in imaging process. Currently, the PI is working in an interdisciplinary area. The PI is planning to offer an interdisciplinary course "Geometric flow in imaging process" next year. The PI is attracting some undergraduate students into his research. The training in research will have great impact on these young people's future career.