Related papers: A K-energy functional for complexified K\"ahler cl…

The four-dimensional effective theory for type IIB warped flux compactifications proposed in [1] is completed by taking into account the backreaction of the K\"ahler moduli on the three-form fluxes. The only required modification consists…

Let (X,L) be a polarized projective complex manifold. We show, by a simple toric one-dimensional example, that Mabuchi's K-energy functional on the geodesically complete space of bounded positive (1,1)-forms in the first Chern class of L,…

In this note, we study a degenerate twisted J-flow on compact K\"ahler manifolds. We show that it exists for all time, it is unique and converges to a weak solution of a degenerate twisted J-equation. In particular, this confirms an…

We investigate a flat Friedmann-Robertson-Walker spacetime filled with k-essence and find the set of functions F which generate three different families of extended tachyon fields and Chaplygin gases. They lead to accelerated and…

We introduce a notion of a K\"ahler metric with constant weighted scalar curvature on a compact K\"ahler manifold $X$, depending on a fixed real torus $\mathbb{T}$ in the reduced group of automorphisms of $X$, and two smooth (weight)…

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…

Let (X,L) be a polarized K\"ahler manifold that admits an extremal K\"ahler metric in c1(L). We show that on a nearby polarized deformation that preserves the symmetry induced by the extremal vector field of (X,L), the modified K-energy is…

Inspired by the work of Z. Lu and G. Tian [8], A. Loi, F. Salis and F. Zuddas address in [5] the problem of studying those K\"ahler manifolds satisfying the $\Delta$-property, i.e. such that on a neighborhood of each of its points the…

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…

Refining Yau's and Kolodziej's techniques, we establish very precise uniform a priori estimates for degenerate complex Monge-Amp\`ere equations on compact K\"ahler manifolds, that allow us to control the blow up of the solutions as the…

We introduce a weighted version of the pluripotential theory on complex K\"{a}hler manifolds developed by Guedj and Zeriahi. We give the appropriate definition of a weighted pluricomplex Green function, its basic properties and consider its…

We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…

We prove that if a compact smooth polarized complex manifold admits in the corresponding Hodge K\"ahler class a conformally K\"ahler, Einstein--Maxwell metric, or more generally, a K\"ahler metric of constant $(\xi, a, p)$-scalar curvature,…

We prove the convergence of geodesic distance during the quantization of the space of K\"ahler potentials. As applications, this provides alternative proofs of certain inequalities about the K-energy functional in the projective case.

We show how affine and projective special K\"ahler manifolds emerge from the structure of quantization. We quantize them and construct natural (wavefunction) representations for the corresponding coherent states. These in turn are shown to…

Consider a divisor D with simple normal crossings in a compact K\"ahler manifold X. We show in this article that a K\"ahler metric in an arbitrary class, with constant scalar curvature and cusp singularities along the divisor is unique in…

We show that degenerate complex Monge-Ampere equations in a big cohomology class of a compact Kaehler manifold can be solved using a variational method independent of Yau's theorem. Our formulation yields in particular a natural…

In this work we define a deformation theory for the Coupled K\"ahler-Yang-Mills equations in arXiv:1102.0991, generalizing work of Sz\'ekelyhidi on constant scalar curvature K\"ahler metrics. We use the theory to find new solutions of the…

We propose an exactly-solvable model of the quantum oscillator on the class of K\"ahler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum…

We prove the uniqueness, up to a pull-back by an element of a suitable subgroup of complex automorphisms, of the weighted extremal K\"ahler metrics on a compact K\"ahler manifold introduced in our previous work. This extends a result by…