126 citations · 174 across the 19 of their papers we have counts for
17 papers · 1 filter
Integral Gauss formula and the Poisson equation for the -Laplacian
Timothy Buttsworth, Stepan Hudecek, Artem Pulemotov
We produce a formula, analogous to the Gauss-Codazzi equation, which relates the geometry of a -structure and its Hodge Laplacian to the geometry of the induced -struct…
Hermitian metrics with vanishing second Chern Ricci curvature
Kyle Broder, Artem Pulemotov
We describe a rigidity phenomenon exhibited by the second Chern Ricci curvature of a Hermitian metric on a compact complex manifold. This yields a characterisation of second Chern…
Palais-Smale sequences for the prescribed Ricci curvature functional
Artem Pulemotov, Wolfgang Ziller
We obtain a complete description of divergent Palais-Smale sequences for the prescribed Ricci curvature functional on compact homogeneous spaces. As an application, we prove the ex…
Local solvability of the Poisson equation for closed -structures
Timothy Buttsworth, Artem Pulemotov
We prove local solvability of the Poisson equation with a positive or negative right-hand side for closed -structures.
On the variational properties of the prescribed Ricci curvature functional
Artem Pulemotov, Wolfgang Ziller
We study the prescribed Ricci curvature problem for homogeneous metrics. Given a (0,2)-tensor field , this problem asks for solutions to the equation for so…
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…
The prescribed Ricci curvature problem for naturally reductive metrics on non-compact simple Lie groups
Romina M. Arroyo, Mark D. Gould, Artem Pulemotov
We investigate the prescribed Ricci curvature problem in the class of left-invariant naturally reductive Riemannian metrics on a non-compact simple Lie group. We obtain a number of…
The prescribed Ricci curvature problem for naturally reductive metrics on compact Lie groups
Romina M. Arroyo, Artem Pulemotov, Wolfgang Ziller
We study the problem of prescribing the Ricci curvature in the class of naturally reductive metrics on a compact Lie group. We derive necessary as well as sufficient conditions for…
The Prescribed Ricci Curvature Problem for Homogeneous Metrics
Timothy Buttsworth, Artem Pulemotov
The prescribed Ricci curvature problem consists in finding a Riemannian metric on a manifold such that the Ricci curvature of equals a given -tensor field . W…
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…
The Prescribed Ricci Curvature Problem on Homogeneous Spaces with Intermediate Subgroups
Mark Gould, Artem Pulemotov
Consider a compact Lie group and a closed subgroup . Suppose is the set of -invariant Riemannian metrics on the homogeneous space . We obtain a suff…
Ricci iteration on homogeneous spaces
Artem Pulemotov, Yanir A. Rubinstein
The Ricci iteration is a discrete analogue of the Ricci flow. We give the first study of the Ricci iteration on a class of Riemannian manifolds that are not Kähler. The Ricci itera…
Metrics with Prescribed Ricci Curvature on Homogeneous Spaces
Artem Pulemotov
Let be a compact connected Lie group and a closed subgroup of . Suppose the homogeneous space is effective and has dimension 3 or higher. Consider a -invariant,…
Metrics with Prescribed Ricci Curvature near the Boundary of a Manifold
Artem Pulemotov
Suppose is a manifold with boundary. Choose a point . We investigate the prescribed Ricci curvature equation $\Ric(G)=T$ in a neighborhood of under natural…
Gradient estimates for the heat equation under the Ricci flow
Mihai Bailesteanu, Xiaodong Cao, Artem Pulemotov
The paper considers a manifold evolving under the Ricci flow and establishes a series of gradient estimates for positive solutions of the heat equation on . Among other resu…
The Li-Yau-Hamilton Estimate and the Yang-Mills Heat Equation on Manifolds with Boundary
Artem Pulemotov
The paper pursues two connected goals. Firstly, we establish the Li-Yau-Hamilton estimate for the heat equation on a manifold with nonempty boundary. Results of this kind are t…
The Hopf Boundary Point Lemma for Vector Bundle Sections
Artem Pulemotov
The paper establishes a version of the Hopf boundary point lemma for sections of a vector bundle over a manifold with boundary. This result may be viewed as a counterpart to the te…