3 papers
math.DG2024
Geometric and Analytic Aspects of Simon-Lojasiewicz Inequalities on Vector Bundles
Owen Drummond
In real analysis, the Lojasiewicz inequalities, revitalized by Leon Simon in his pioneering work on singularities of energy minimizing maps, have proven to be monumental in differe…
math.AP2024
The Top Dimensional Singular Set
Owen Drummond
In this survey, we examine the properties of the top dimensional singular set , including several theorems, geometric properties, and relation to homogeneous de…
math.AP2024
Geometric Analysis of Energy Minimizing Maps: Tangent Maps and Singularities
Owen Drummond
Energy minimizing maps (E.M.M.s) play a central role in the calculus of variations, partial differential equations (PDEs), and geometric analysis. These maps are often embedded int…