4 papers
Quantitative Rigidity Using Colding's Monotonicity Formulas for Ricci Curvature
Christine Breiner, Jiewon Park
In \cite{Colding}, Colding proved monotonicity formulas for the Green function on manifolds with nonnegative Ricci curvature. Inspired by the sharp estimates relating the pinching…
Harmonic Maps into Euclidean Buildings and Non-Archimedean Superrigidity
Christine Breiner, Ben K. Dees, Chikako Mese
We prove that harmonic maps into Euclidean buildings, which are not necessarily locally finite, have singular sets of Hausdorff codimension 2, extending the locally finite regulari…
On the Possible Orders of Harmonic Maps into Euclidean Buildings
Christine Breiner, Ben K. Dees
We prove a discreteness result for the possible orders of harmonic maps from surfaces to Euclidean buildings; in particular for a building of type the order is of the form $\fr…
Rectifiability of the singular strata for harmonic maps to Euclidean buildings
Christine Breiner, Ben K. Dees
We define a natural notion of the singular strata for harmonic maps into -connected complexes (which include locally finite Euclidean buildings), and prove the rectifiability of…