Timothy Buttsworth

activity

20172026

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12 papers · 1 filter

math.DG2026

Integral Gauss formula and the Poisson equation for the $G_{2}$ -Laplacian

Timothy Buttsworth, Stepan Hudecek, Artem Pulemotov

We produce a formula, analogous to the Gauss-Codazzi equation, which relates the geometry of a $G_{2}$ -structure and its Hodge Laplacian to the geometry of the induced $S U (3)$ -struct…

math.DG2026

Incompressible Euler fluids on compact cohomogeneity one manifolds

Timothy Buttsworth, Max Orchard

Let $(M, g)$ be a connected and compact Riemannian manifold admitting an isometric action by a compact Lie group $G$ whose principal orbits have codimension one. We show th…

math.DG2024

Computationally-assisted proof of a novel $O (3) \times O (10)$ -invariant Einstein metric on $S^{12}$

Timothy Buttsworth, Liam Hodgkinson

We prove existence of a non-round Einstein metric $g$ on $S^{12}$ that is invariant under the usual cohomogeneity one action of $O (3) \times O (10)$ on $S^{12}\subse…

math.DG2023

Scalar curvature along Ebin geodesics

Christoph Böhm, Timothy Buttsworth, Brian Clarke

Let $M$ be a smooth, compact manifold and let $N_{μ}$ denote the set of Riemannian metrics on $M$ with smooth volume density $μ$ . For a given $g_{0} \in N_{μ}$ , we sho…

math.DG2023

Local solvability of the Poisson equation for closed $G_{2}$ -structures

Timothy Buttsworth, Artem Pulemotov

We prove local solvability of the Poisson equation with a positive or negative right-hand side for closed $G_{2}$ -structures.

math.DG2023

Ancient Ricci flows of bounded girth

Theodora Bourni, Timothy Buttsworth, Ramiro Lafuente +1

For each $n \geq 3$ , we construct a 'pancake-like', $O (2) \times O (n - 1)$ -invariant ancient Ricci flow with positive curvature operator and bounded "girth", and we determine its asympt…

Integral Gauss formula and the Poisson equation for the G2​-Laplacian

Incompressible Euler fluids on compact cohomogeneity one manifolds

Computationally-assisted proof of a novel O(3)×O(10)-invariant Einstein metric on S12

Scalar curvature along Ebin geodesics

Local solvability of the Poisson equation for closed G2​-structures

Ancient Ricci flows of bounded girth

Integral Gauss formula and the Poisson equation for the $G_{2}$ -Laplacian

Computationally-assisted proof of a novel $O (3) \times O (10)$ -invariant Einstein metric on $S^{12}$

Local solvability of the Poisson equation for closed $G_{2}$ -structures