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math.DG2025
Deficit functions and the log Sobolev inequality
Tobias Holck Colding, William P. Minicozzi
There is a long history of parabolic monotonicity formulas that developed independently from several different fields and a much more recent elliptic theory. The elliptic theory ca…
math.DG2025
Quantitative uniqueness for mean curvature flow
Tobias Holck Colding, William P. Minicozzi
We show how to use the arguments of [CM2] to get a stronger effective version of uniqueness of blowups that has a number of consequences.
math.DG2025★ 1 cited
Gradient estimates for scalar curvature
Tobias Holck Colding, William P. Minicozzi
A gradient estimate is a crucial tool used to control the rate of change of a function on a manifold, paving the way for deeper analysis of geometric properties. A celebrated resul…