Panagiotis Gianniotis

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20172025

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math.DG2025

$L^{1}$ curvature bounds for Type I Ricci flows

Panagiotis Gianniotis, Konstantinos Leskas

We show $L^{1}$ -bounds of the Riemann curvature tensor on a smooth closed $n$ -dimensional Ricci flow. To achieve this we introduce the notion of a neck of maximal symmetry, similar t…

math.DG2025

Diameter bounds in 3d Type I Ricci flows

Panagiotis Gianniotis

We prove that a three dimensional compact Ricci flow that encounters a Type I singularity has uniformly bounded diameter up to the singular time, thus giving an affirmative answer…

math.DG2025

A $G_{2}$ -Hilbert functional in $G_{2}$ -geometry

Panagiotis Gianniotis, George Zacharopoulos

In this paper we introduce a new functional on the space of $G_{2}$ -structures which we call the $G_{2}$ -Hilbert functional. It is uniquely determined by a few basic principles inspire…

math.DG2019

A gradient flow of isometric $G_{2}$ structures

Shubham Dwivedi, Panagiotis Gianniotis, Spiro Karigiannis

We study a flow of $G_{2}$ structures which induce the same Riemannian metric which is the negative gradient flow of an energy functional. We prove Shi-type estimates for the torsion…

math.DG2017

Diameter and curvature control under mean curvature flow

Panagiotis Gianniotis, Robert Haslhofer

We prove that for the mean curvature flow of two-convex hypersurfaces the intrinsic diameter stays uniformly controlled as one approaches the first singular time. We also derive sh…

L1 curvature bounds for Type I Ricci flows

Diameter bounds in 3d Type I Ricci flows

A G2​-Hilbert functional in G2​-geometry

A gradient flow of isometric G2​ structures

Diameter and curvature control under mean curvature flow

$L^{1}$ curvature bounds for Type I Ricci flows

A $G_{2}$ -Hilbert functional in $G_{2}$ -geometry

A gradient flow of isometric $G_{2}$ structures