12 citations · 18 across the 6 of their papers we have counts for
6 papers
Parabolic frequency for the mean curvature flow
Julius Baldauf, Tang-Kai Lee
This paper defines a parabolic frequency for solutions of the heat equation along homothetically shrinking mean curvature flows and proves its monotonicity along such flows. As a c…
Harmonic spinors in the Ricci flow
Julius Baldauf
This paper studies the Ricci flow on closed manifolds admitting harmonic spinors. It is shown that Perelman's Ricci flow entropy can be expressed in terms of the energy of harmonic…
The spinorial energy for asymptotically Euclidean Ricci flow
Julius Baldauf, Tristan Ozuch
This paper introduces a functional generalizing Perelman's weighted Hilbert-Einstein action and the Dirichlet energy for spinors. It is well-defined on a wide class of non-compact…
Parabolic frequency on Ricci flows
Julius Baldauf, Dain Kim
This paper defines a parabolic frequency for solutions of the heat equation on a Ricci flow and proves it's monotonicity along the flow. Frequency monotonicity is known to have man…
Spinors and mass on weighted manifolds
Julius Baldauf, Tristan Ozuch
This paper generalizes classical spin geometry to the setting of weighted manifolds (manifolds with density) and provides applications to the Ricci flow. Spectral properties of the…
Sharp Entropy Bounds for Plane Curves and Dynamics of the Curve Shortening Flow
Julius Baldauf, Ao Sun
We prove that a closed immersed plane curve with total curvature has entropy at least times the entropy of the embedded circle, as long as it generates a type I singulari…