2 papers
math.DG2025
Deriving Perelman's entropy from Colding's monotonic volume
Ignacio Bustamante, Martin Reiris
In his groundbreaking work from 2002, Perelman introduced two fundamental monotonic quantities: the reduced volume and the entropy. While the reduced volume was motivated by the Bi…
math.AP2025
A monotonicity formula for a semilinear fractional parabolic equation
Ignacio Bustamante
We apply a high-dimensional parabolic-to-elliptic transformation to the fully fractional, semilinear heat equation , where and , and…