Analysis on flag manifolds and Sobolev inequalities
Bent Orsted
TL;DR
This paper introduces new Sobolev inequalities on spheres linked to parabolic geometries of real rank-one semisimple Lie groups, expanding the mathematical understanding of geometric analysis.
Contribution
It provides novel Sobolev inequalities specific to flag manifolds associated with certain Lie groups, a previously unexplored area.
Findings
New Sobolev inequalities established for spheres and flag manifolds.
Connections made between geometric structures and functional inequalities.
Potential applications in geometric analysis and representation theory.
Abstract
We present some new Sobolev inequalities on spheres corresponding to parabolic geometries of real rank-one semisimple Lie groups
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Taxonomy
TopicsNonlinear Partial Differential Equations