Related papers: Energy functionals and K\"ahler-Ricci solitons

The limiting behavior of the normalized K\"ahler-Ricci flow for manifolds with positive first Chern class is examined under certain stability conditions. First, it is shown that if the Mabuchi K-energy is bounded from below, then the scalar…

In [David-Toro 15] and [David-Engelstein-Toro 19], (some of) the authors studied almost minimizers for functionals of the type first studied by Alt and Caffarelli in [Alt-Caffarelli 81] and Alt, Caffarelli and Friedman in…

We introduce a class of almost homogeneous varieties contained in the class of spherical varieties and containing horospherical varieties as well as complete symmetric varieties. We develop K{\"a}hler geometry on these varieties, with…

The Ricci iteration is a discrete analogue of the Ricci flow. According to Perelman, the Ricci flow converges to a Kahler-Einstein metric whenever one exists, and it has been conjectured that the Ricci iteration should behave similarly.…

Let $(X, D)$ be a log variety with an effective holomorphic torus action, and $\Theta$ be a closed positive $(1,1)$-current. For any smooth positive function $g$ defined on the moment polytope of the torus action, we study the…

In this article we study lower semicontinuous, convex functionals on real Hilbert spaces. In the first part of the article we construct a Banach space that serves as the energy space for such functionals. In the second part we study…

In this note we provide a proof of the following: Any compact KRS with positive bisectional curvature is biholomorphic to the complex projective space. As a corollary, we obtain an alternative proof of the Frankel conjecture by using the…

We show that integrability of an almost complex structure in complex dimension $m$ is equivalent, in the presence of an almost hermitian metric, to $m(m-1)$ equations involving what we call shear operators. Inspired by this, we give an…

This paper studies a non-trivial gradient K\"{a}hler-Ricci soliton, of complex dimension $n$, with an isometry group of dimension at least $n^2-1$. We show that the isometry group acts by cohomogeneity one and, consequently, admits a…

Over the space of K\"ahler metrics associated to a fixed K\"ahler class, we first prove the lower bound of the energy functional $\tilde E^\beta$, then we provide the criterions of the geodesics rays to detect the lower bound of $\tilde…

We investigate the Kahler-Ricci flow on holomorphic fiber spaces whose generic fiber is a Calabi-Yau manifold. We establish uniform metric convergence to a metric on the base, away from the singular fibers, and show that the rescaled…

If a normalized K\"{a}hler-Ricci flow $g(t),t\in[0,\infty),$ on a compact K\"{a}hler $n$-manifold, $n\geq 3$, of positive first Chern class satisfies $g(t)\in 2\pi c_{1}(M)$ and has $L^{n}$ curvature operator uniformly bounded, then the…

We construct a family of non-collapsed, non-K\"ahler, non-Einstein steady Ricci solitons in even dimensions greater or equal to four. These solitons exist on complex line bundles over K\"ahler-Einstein manifolds of positive scalar…

We prove that the correspondence between Reeb and Beltrami vector fields can be made equivariant whenever additional symmetries of the underlying geometric structures are considered. As a corollary of this correspondence, we show that…

We study the energy functional on the set of Lagrangian tori in $\mathbb{C}P^2$ . We prove that the value of the energy functional on a certain family of Hamiltonian minimal Lagrangian tori in $\mathbb{C}P^2$ is strictly larger than energy…

In this paper we introduce, in the Riemannian setting, the notion of conformal Ricci soliton, which includes as particular cases Einstein manifolds, conformal Einstein manifolds and (generic and gradient) Ricci solitons. We provide here…

In this work, we obtain a existence criteria for the longtime K\"ahler Ricci flow solution. Using the existence result, we generalize a result by Wu-Yau on the existence of K\"ahler Einstein metric to the case with possibly unbounded…

In this paper, we prove that a gradient shrinking compact K\"ahler-Ricci soliton cannot have too large Ricci curvature unless it is K\"ahler-Einstein.

Koopmans-compliant (KC) functionals have been shown to provide accurate spectral properties through a generalized condition of piece-wise linearity of the total energy as a function of the fractional addition/removal of an electron to/from…

In this note two results are established for energy functionals that are given by the integral of $ W(\mathbf x,\nabla \mathbf u(\mathbf x))$ over $\Omega \subset\mathbb{R}^n$ with $\nabla \mathbf u \in BMO(\Omega;{\mathbb R}^{N\times n})$,…