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math.AP2025
Directional Poincaré inequality on compact Lie groups
Paulo L. Dattori da Silva, André Pedroso Kowacs
We extend the directional Poincaré inequality on the torus, introduced by Steinerberger in [Ark. Mat. 54 (2016), pp. 555--569], to the setting of compact Lie groups. We provide nec…
math.DS2025
On the Piecewise Holomorphic Systems with Three Zones
Carlos Vinicius das Neves Silva, Paulo Ricardo da Silva
We study piecewise-smooth systems with three zones, , whose discontinuity set consists either of a pair of parallel lines or a pair of circles ta…