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math.DG2026
Volume Growth under Positive Intermediate Curvature and a Ricci Lower Bound
Robert Koirala
Let be a complete Riemannian manifold with $\Ric\ge-kg$ and uniformly positive -intermediate curvature in the sense of Brendle--Hirsch--Johne. We prove that the Fisher…
math.DG2026
The Fisher Metric of the Ricci Flow Heat Kernel
Bennett Chow, Robert Koirala
We introduce and study a Fisher information metric \(g^F_τ\) associated to the conjugate heat kernel of a Ricci flow \((M^n,g_t)\). This tensor measures, at a fixed scale, how the…
math.DG2026
Sharp Gaussian Isoperimetry along a Ricci Flow
Robert Koirala
We prove the sharp Gaussian isoperimetric inequality for conjugate heat-kernel measures along a Ricci flow via a monotonicity formula. As consequences, we obtain the exact Gaussian…