Panagiotis Gianniotis

collaborators

5 papers

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

Splitting maps in Type I Ricci flows

Panagiotis Gianniotis

We study the existence and small scale behaviour of almost splitting maps along a Ricci flow satisfying Type I curvature bounds. These are special solutions of the heat equation th…

math.DG2025

Flows of $G_{2}$ -structures, II: Curvature, torsion, symbols, and functionals

Shubham Dwivedi, Panagiotis Gianniotis, Spiro Karigiannis

We continue the investigation of general geometric flows of $G_{2}$ -structures initiated by the third author in "Flows of $G_{2}$ -structures, I." Specifically, we determine the possibl…

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…

L1 curvature bounds for Type I Ricci flows

Diameter bounds in 3d Type I Ricci flows

Splitting maps in Type I Ricci flows

Flows of G2​-structures, II: Curvature, torsion, symbols, and functionals

A G2​-Hilbert functional in G2​-geometry

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

Flows of $G_{2}$ -structures, II: Curvature, torsion, symbols, and functionals

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