Related papers: Energy functionals on almost K\"ahler manifolds: I

The goal of this expository article is to explain how a fundamental functional on the space of Jordan curves arising from SLE - Loewner energy - is connected to a seemingly far apart subject: the K\"ahler geometry of universal Teichm\"uller…

We survey some recent results and constructions of almost-K\"ahler manifolds whose curvature tensors have certain algebraic symmetries. This is an updated and corrected version of the (to be) published manuscript.

In this short note, we show that given a special K\"ahler-Einstein degeneration with bounded geometry, for any noncentral fiber, there exists a K\"ahler-Ricci flow which converges to the K\"ahler-Einstein metric of the central fiber. As an…

In this paper, we consider maps from pseudo-Hermitian manifolds to K\"{a}hler manifolds and introduce partial energy functionals for these maps. First, we obtain a foliated Lichnerowicz type result on general pseudo-Hermitian manifolds,…

In this survey, we give an introduction to nearly K\"ahler geometry, and list some results on submanifolds of these spaces. This survey tries by no means to be complete.

Common density-matrix functionals, the M\"uller and the power functional, have been benchmarked for the half-filled Hubbard dimer, which allows to model the bond dissociation problem and the transition from the weakly to the strongly…

Many contact metric manifolds are critical points of curvature functionals restricted to spaces of associated metrics. The Godbillon-Vey functional has never been considered in a variational context in contact geometry. Recently we extended…

Duality is an indispensable tool for describing the strong-coupling dynamics of gauge theories. However, its actual realization is often quite subtle: quantities such as the partition function can transform covariantly, with degrees of…

Recently, Donaldson proved asymptotic stability for a polarized algebraic manifold $M$ with polarization class admitting a K\"ahler metric of constant scalar curvature, essentially when the linear algebraic part $H$ of $Aut^0(M)$ is…

Let \(\mathcal{G}\) be a non-empty subset of the Euclidean space \(\mathbb{R}^m\) (\(m \geq 1\)). This work is dedicated to further exploring the properties of \(\mathcal{G}\)-multi-almost automorphic functions defined on \(\mathbb{R}^m\)…

In this work we investigate Ricci flows of almost Kaehler structures on Lie algebroids when the fundamental geometric objects are completely determined by (semi) Riemannian metrics, or effective) regular generating Lagrange/ Finsler,…

In this paper we construct Mabuchi $\mathcal{L}^{{\rm M}}_{\omega}$ functional and Aubin-Yau functionals $\mathcal{I}^{{\rm AY}}_{\omega}, \mathcal{J}^{{\rm AY}}_{\omega}$ on any compact complex three-folds. The method presented here will…

We study finite energy classes of quasiplurisubharmonic (qpsh) functions in the setting of toric compact K{\"a}hler manifolds. We characterize toric qpsh functions and give necessary and sufficient conditions for them to have finite…

It is shown that geodesics in the space of K\"ahler potentials can be uniformly approximated by geodesics in the spaces of Bergman metrics. Two important tools in the proof are the Tian-Yau-Zelditch approximation theorem for K\"ahler…

In this note, we shall prove geodesic convexity of the space of K\"ahler potentials on an ALE K\"ahler manifold. This extends earlier results in the compact case proved in the fundamental work of X-X. Chen. We further prove the boundedness…

Consider a compact K\"ahler manifold $(X,\omega)$ and the space $\cal E(X,\omega)=\cal E$ of $\omega$--plurisubharmonic functions of full Monge--Amp\`ere mass on it. We introduce a quantity $\rho[u,v]$ to measure the distance between $u,…

In this paper, we introduce the stress-energy tensors of the partial energies E'(f) and E"(f) of maps between Kaehler manifolds. Assuming the domain manifolds poss some special exhaustion functions, we use these stress-energy tensors to…

This note discusses the higher K-energy functionals which were defined by Bando and Mabuchi, and integrate higher Futaki invariants. Two new formulas for the higher K-energy functionals are given, and the second K-energy is shown to be…

Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex valued Ray-Singer…

We study the map from conductances to edge energies for harmonic functions on finite graphs with Dirichlet boundary conditions. We prove that for any compatible acyclic orientation and choice of energies there is a unique choice of…