Project information

Project information
Smooth and analytic regularity in CR geometry (SARCG)

Project Identification
Project Period
1/2022 - 12/2024
Investor / Pogramme / Project type
Czech Science Foundation
MU Faculty or unit
Faculty of Science
Cooperating Organization
University of Sao Paulo

Among the most exciting developments in PDEs in the last few decades is the interplay
between CR (Cauchy-Riemann) geometry, as a branch of Complex Analysis, and the general
theory of locally integrable PDE systems, going back to the classical work of Hörmander, H.
Lewy, Nirenberg, Treves. The main goal of this project is to push this interplay further. We will
study the solvability (exactness) of the tangential Cauchy-Riemann complex on classes of
generic submanifolds of the complex space, and investigate regularity problems for CR-maps
between submanifolds. We will study local, semi-global and global solvability, and for CR-maps
their analytic and Gevrey regularity. The novelty of the approach is to bring techniques from the
general theory of locally integrable structures. We as well plan extending regularity phenomena
from the CR-case to more general structures. We will put together the close but still
complimentary expertise of the Czech team, specializing on CR-geometry, and the Sao Paulo
team, specializing on the general theory of locally integrable structures.


Total number of publications: 1

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