8 citations · 25 across the 14 of their papers we have counts for
17 papers
Regularizing estimates for positive solutions of the heat equation under geometric flows
Alessandro Goffi, Francesco Pediconi
We study higher-order global estimates for the heat equation on Riemannian manifolds, both for static metrics and for metrics evolving under the Ricci flow. Under minimal geometric…
Yamabe-type problems on compact Hermitian manifolds
Daniele Angella, Francesco Pediconi, Carlo Scarpa +2
We introduce and study a one-parameter Hermitian deformation of the Yamabe problem on compact complex manifolds. The deformation is defined by adding natural torsion terms to the R…
On the long time behavior of ancient homogeneous Ricci flows
Anusha M. Krishnan, Francesco Pediconi
We prove a precompactness theorem for invariant metrics on compact homogeneous spaces without injectivity radius bounds, assuming uniform bounds on the diameter and on all derivati…
Toral symmetries of collapsed ancient solutions to the homogeneous Ricci flow
Anusha M. Krishnan, Francesco Pediconi, Sammy Sbiti
Collapsed ancient solutions to the homogeneous Ricci flow on compact manifolds occur only on the total space of principal torus bundles. Under an algebraic assumption that guarante…
A moment map for twisted-Hamiltonian vector fields on locally conformally Kähler manifolds
Daniele Angella, Simone Calamai, Francesco Pediconi +1
We extend the classical Donaldson-Fujiki interpretation of the scalar curvature as moment map in Kähler Geometry to the wider framework of locally conformally Kähler Geometry.
A survey on locally Homogeneous almost-Hermitian spaces
Daniele Angella, Francesco Pediconi
We survey the theory of locally homogeneous almost-Hermitian spaces. In particular, by using the framework of varying Lie brackets, we write formulas for the curvature of all the G…
Sobolev regularity for nonlinear Poisson equations with Neumann boundary conditions on Riemannian manifolds
Alessandro Goffi, Francesco Pediconi
In this paper, we study the Sobolev regularity of solutions to nonlinear second order elliptic equations with super-linear first-order terms on Riemannian manifolds, complemented w…
Collapsed ancient solutions of the Ricci flow on compact homogeneous spaces
Francesco Pediconi, Sammy Sbiti
We prove a general existence theorem for collapsed ancient solutions to the Ricci flow on compact homogeneous spaces and we show that they converge in the Gromov-Hausdorff topology…
On the linearization stability of the Chern-scalar curvature
Daniele Angella, Francesco Pediconi
In this note, we study the local properties of the Chern-scalar curvature function by looking at its linearization. In particular, we study its linearization stability and the stru…
On cohomogeneity one Hermitian non-Kähler metrics
Daniele Angella, Francesco Pediconi
We investigate the geometry of Hermitian manifolds endowed with a compact Lie group action by holomorphic isometries with principal orbits of codimension one. In particular, we foc…
A note on the strong maximum principle for fully nonlinear equations on Riemannian manifolds
Alessandro Goffi, Francesco Pediconi
We investigate strong maximum (and minimum) principles for fully nonlinear second order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate sc…
Convergence of locally homogeneous spaces
Francesco Pediconi
We study three different topologies on the moduli space of equivariant isometry classes of -dimensional locally homogeneous Riemannian spaces. As an ap…
A compactness theorem for locally homogeneous spaces
Francesco Pediconi
We prove the existence and uniqueness of geometric models of local isometry classes of locally homogeneous spaces with sectional curvature . Moreover, w…
Hermitian curvature flow on complex locally homogeneous surfaces
Francesco Pediconi, Mattia Pujia
We study the Hermitian curvature flow of locally homogeneous non-Kähler metrics on compact complex surfaces. In particular, we characterize the long-time behavior of the solutions…
A local version of the Myers-Steenrod Theorem
Francesco Pediconi
We prove the Myers-Steenrod theorem for local topological groups of isometries acting on pointed -Riemannian manifolds, with . As an application, we infer…
Diverging sequences of unit volume invariant metrics with bounded curvature
Francesco Pediconi
We study 1-parameter families in the space of -invariant, unit volume metrics on a given compact, connected, almost-effective homogeneous space . In par…
Chern-Dirac bundles on non-Kähler Hermitian manifolds
Francesco Pediconi
We introduce the notions of Chern-Dirac bundles and Chern-Dirac operators on Hermitian manifolds. They are analogues of classical Dirac bundles and Dirac operators, with Levi-Civit…