Various notions of convexity of sets and functions in the Heisenberg group have been studied in the past two decades. In this talk, we focus on the horizontally quasiconvex (h-quasiconvex) functions in the Heisenberg group. Inspired by the first- order characterization and construction of quasiconvex envelope by Barron, Goebel and Jensen in the Euclidean space, we obtain a PDE approach to construct the h-quasiconvex envelope for a given function f in the Heisenberg group. In particular, we show the uniqueness and existence of viscosity solutions to a non-local Hamilton-Jacobi equation and iterate the equation to obtain the h-quasiconvex envelope. Relations between h- convex hull of a set and the h-quasiconvex envelopes are also investigated. This is joint work with Antoni Kijowski (OIST) and Qing Liu (Fukuoka University/OIST).

25 Mar 2022
9am - 10am
Where
https://hkust.zoom.us/j/98049654261 (Passcode: 495913)
Speakers/Performers
Prof. Xiaodan ZHOU
Okinawa Institute of Science and Technology Graduate University
Organizer(S)
Department of Mathematics
Contact/Enquiries
Payment Details
Audience
Alumni, Faculty and staff, PG students, UG students
Language(s)
English
Other Events
26 Apr 2024
Seminar, Lecture, Talk
IAS / School of Science Joint Lecture - Molecular Basis of Wnt Biogenesis, Secretion and Ligand Specific Signaling
Abstract Wnt signaling is essential to regulate embryonic development and adult tissue homeostasis. Aberrant Wnt signaling is associated with cancers. The ER-resident membrane-bound O-acyltransfera...
18 Apr 2024
Seminar, Lecture, Talk
IAS / School of Science Joint Lecture - Understanding the Roles of Transposable Elements in the Human Genome
Abstract Transposable elements (TEs) have expanded the binding repertoire of many transcription factors and, through this process, have been co-opted in different transcriptional networks. In this ...