From the 1 of 4 linked papers with an AI index.
4 papers
A short note on the dimension of the CC-geodesic Kakeya sets in the first Heisenberg group
Marianna Chatzakou
The paper studies Kakeya sets built from left translates of unit‑speed Carnot–Carathéodory geodesic segments in the first Heisenberg group, proving that the sharp lower bound for t…
Fujita exponent for heat equation with Hörmander vector fields
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper, we show global existence and non-existence results for the heat equation with some of the squares of smooth vector fields on $\Rn$ satisfying Hörmander's rank condi…
Zero modes and Dirac-(logarithmic) Sobolev-type inequalities
Marianna Chatzakou, Uwe Kahler, Michael Ruzhansky
We study the decay rate of the zero modes of the Dirac operator with a matrix-valued potential that is considered here without any regularity assumptions, compared to the existing…
Nearness and solvability of non-invariant equations on stratified groups
Marianna Chatzakou, Michael Ruzhansky, Nikos Yannakakis
We prove the well-posedness of the differential equation in the setting of a stratified group when the considered second-order differential operator can be…