Topics in Geometry: In Memory of Joseph D'Atri

This work delves into the field of geometry, paying tribute to the influential mathematician Joseph D'Atri through a collection of topics that resonate with his legacy. The author, S.G. Gindikin, explores complex themes such as non-linear elliptic equations within the framework of Riemannian manifolds, particularly highlighting the Sobolev critical exponent.

As readers navigate through the intricate discussions and findings, they encounter a blend of theoretical insights and applied mathematics, contributing to the broader understanding of geometric analysis. This compilation serves not only as an academic resource but also as an homage to D'Atri’s contributions to the field, inspiring both seasoned mathematicians and newcomers alike.