Volume 54, Issue 1
Isoperimetric Type Inequalities and Hypersurface Flows

Pengfei Guan & Junfang Li

J. Math. Study, 54 (2021), pp. 56-80.

Published online: 2021-01

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  • Abstract

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.

  • AMS Subject Headings

53C23, 53C42, 35J60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

guan@math.mcgill.ca (Pengfei Guan)

jfli@uab.edu (Junfang Li)

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@Article{JMS-54-56, author = {Guan , Pengfei and Li , Junfang}, title = {Isoperimetric Type Inequalities and Hypersurface Flows}, journal = {Journal of Mathematical Study}, year = {2021}, volume = {54}, number = {1}, pages = {56--80}, abstract = {

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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v54n1.21.03}, url = {http://global-sci.org/intro/article_detail/jms/18598.html} }
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 -

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.

Pengfei Guan & Junfang Li. (2021). Isoperimetric Type Inequalities and Hypersurface Flows. Journal of Mathematical Study. 54 (1). 56-80. doi:10.4208/jms.v54n1.21.03
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