TY - JOUR
T1 - Isoperimetric Type Inequalities and Hypersurface Flows
AU - Guan , Pengfei
AU - Li , Junfang
JO - Journal of Mathematical Study
VL - 1
SP - 56
EP - 80
PY - 2021
DA - 2021/01
SN - 54
DO - http://doi.org/10.4208/jms.v54n1.21.03
UR - https://global-sci.org/intro/article_detail/jms/18598.html
KW - Hypersurface curvature flows, geometric inequalities,  quermassintegrals.
AB - <p style="text-align: justify;">New types of hypersurface flows have been introduced recently with goals
to establish isoperimetric type inequalities in geometry. These flows serve as efficient
paths to achieve the optimal solutions to the problems of calculus of variations in geometric setting. The main idea is to use variational structures to develop hypersurface
flows which are monotonic for the corresponding curvature integrals (including volume and surface area). These new geometric flows pose interesting but challenging
PDE problems. Resolution of these problems have significant geometric implications.</p>