Timothy Buttsworth

activity

20162026

most citedOn the Ricci iteration for homogeneous metrics on spheres and projective spaces

13 citations · 13 across the 16 of their papers we have counts for

collaborators

20 papers

math.DG2026

The Kähler-Einstein metric on the third Del Pezzo surface

Timothy Buttsworth, William Hadden, Elli Heyes +2

The compact four-dimensional manifold $CP_{2} #3 CP_{2}$ is known to admit a toric Kähler-Einstein metric $g_{KE}$ , but the metric is not known in c…

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…

physics.ins-det2024

Accurate transient heat flux from simple treatment of surface temperature distribution in the semi-infinite case

David Buttsworth, Timothy Buttsworth

When the variations of surface temperature are measured both spatially and temporally, analytical expressions that correctly account for multi-dimensional transient conduction can…

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…

math.DG2022

Canonical surgeries in rotationally invariant Ricci flow

Timothy Buttsworth, Maximilien Hallgren, Yongjia Zhang

We construct a rotationally invariant Ricci flow through surgery starting at any closed rotationally invariant Riemannian manifold. We demonstrate that a sequence of such Ricci flo…

math.DG2021

$S U (2)$ -invariant steady gradient Ricci solitons on four-manifolds

Timothy Buttsworth

Using center manifolds and topological degree theory, we construct a new family of complete, $S U (2)$ -invariant and steady gradient Ricci solitons on the four-dimensional non-compac…

math.DG2021

The prescribed cross curvature problem on the three-sphere

Timothy Buttsworth, Artem Pulemotov

The paper studies the problem of prescribing positive cross curvature on the three-dimensional sphere. We produce several existence results and an example of non-uniqueness, dispro…

math.DG2021

$S O (2) \times S O (3)$ -invariant Ricci solitons and ancient flows on $S^{4}$

Timothy Buttsworth

Consider the standard action of $S O (2) \times S O (3)$ on $R^{5} = R^{2} \oplus R^{3}$ . We establish the existence of a uniform constant $C > 0$ so that any…

math.DG2020

Prescribing Ricci curvature on a Product of Spheres

Timothy Buttsworth, Anusha M. Krishnan

We prove an existence result for the prescribed Ricci curvature equation for certain doubly warped product metrics on $S^{d_{1} + 1} \times S^{d_{2}}$ , where $d_i \geq 2…

physics.ins-det2020

Deducing Flux from Single Point Temperature History when Relative Spatial Variation of Flux is Prescribed

David Buttsworth, Timothy Buttsworth

Surface heat transfer in convective and radiative environments is sometimes measured by recording the surface temperature history in a transient experiment and interpreting this su…

math.DG2019

The Prescribed Ricci Curvature Problem for Homogeneous Metrics

Timothy Buttsworth, Artem Pulemotov

The prescribed Ricci curvature problem consists in finding a Riemannian metric $g$ on a manifold $M$ such that the Ricci curvature of $g$ equals a given $(0, 2)$ -tensor field $T$ . W…

math.DG2019

Local Stability of Einstein Metrics Under the Ricci Iteration

Timothy Buttsworth, Maximilien Hallgren

We provide a sufficient condition for the local stability of closed Einstein manifolds of positive Ricci curvature under the Ricci iteration in terms of the spectrum of the Lichner…

math.DG2018★ 13 cited

On the Ricci iteration for homogeneous metrics on spheres and projective spaces

Timothy Buttsworth, Artem Pulemotov, Yanir A. Rubinstein +1

We study the Ricci iteration for homogeneous metrics on spheres and complex projective spaces. Such metrics can be described in terms of modifying the canonical metric on the fiber…

math.DG2018

Cohomogeneity-One Quasi-Einstein Metrics

Timothy Buttsworth

Let $G / H$ be a connected, simply connected homogeneous space of a compact Lie group $G$ . We study $G$ -invariant quasi-Einstein metrics on the cohomogeneity one manifold $G/H\times…

math.DG2017

The Dirichlet Problem for Einstein Metrics on Cohomogeneity One Manifolds

Timothy Buttsworth

Let $G / H$ be a compact homogeneous space, and let $g^_{0}$ and $g^_{1}$ be $G$ -invariant Riemannian metrics on $G / H$ . We consider the problem of finding a $G$ -invariant Einst…

math.DG2016

The Prescribed Ricci Curvature Problem on Three-Dimensional Unimodular Lie Groups

Timothy Buttsworth

Let G be a three-dimensional unimodular Lie group, and let T be a left-invariant symmetric (0, 2)-tensor field on G. We provide the necessary and sufficient conditions on T for the…

The Kähler-Einstein metric on the third Del Pezzo surface

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

Incompressible Euler fluids on compact cohomogeneity one manifolds

Accurate transient heat flux from simple treatment of surface temperature distribution in the semi-infinite case

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

Canonical surgeries in rotationally invariant Ricci flow

SU(2)-invariant steady gradient Ricci solitons on four-manifolds

The prescribed cross curvature problem on the three-sphere

SO(2)×SO(3)-invariant Ricci solitons and ancient flows on S4

Prescribing Ricci curvature on a Product of Spheres

Deducing Flux from Single Point Temperature History when Relative Spatial Variation of Flux is Prescribed

The Prescribed Ricci Curvature Problem for Homogeneous Metrics

Local Stability of Einstein Metrics Under the Ricci Iteration

On the Ricci iteration for homogeneous metrics on spheres and projective spaces

Cohomogeneity-One Quasi-Einstein Metrics

The Dirichlet Problem for Einstein Metrics on Cohomogeneity One Manifolds

The Prescribed Ricci Curvature Problem on Three-Dimensional Unimodular Lie Groups

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

$S U (2)$ -invariant steady gradient Ricci solitons on four-manifolds

$S O (2) \times S O (3)$ -invariant Ricci solitons and ancient flows on $S^{4}$