Related papers: Properness of log $F$-functionals

The notion of coupled K\"ahler-Einstein metrics was introduced recently by Hultgren-WittNystr\"om. In this paper we discuss deformation of a coupled K\"ahler-Einstein metrics on a Fano manifold. In particular we obtain a necessary and…

We prove the convergence of K\"ahler-Ricci flow with some small initial curvature conditions. As applications, we discuss the convergence of K\"ahler-Ricci flow when the complex structure varies on a K\"ahler-Einstein manifold.

We prove the existence of K\"ahler-Ricci solitons on toric Fano orbifolds, hence extend the the theorem of Wang and Zhu [WZ] to the orbifold case.

On a Fano manifold, we prove that the Kahler-Ricci flow starting from a Kahler metric in the anti-canonical class which is sufficiently close to a Kahler-Einstein metric must converge in a polynomial rate to a Kahler-Einstein metric. The…

We construct a coalescence hidden variable fractal interpolation function (CHFIF) through a non-diagonal iterated function system(IFS). Such a FIF may be self-affine or non-self-affine depending on the parameters of the defining…

We explain a correct proof of the decomposition theorem for direct images of constant Hodge modules by proper K\"ahler morphisms of complex manifolds. We also give some examples showing certain difficulty in the non-constant Hodge module…

In this paper, we study the boundary behavior of the negatively curved K\"ahler-Einstein metric attached to a log canonical pair $(X,D)$ such that $K_X+D$ is ample. In the case where $X$ is smooth and $D$ has simple normal crossings support…

For a standard Finsler metric F on a manifold M, its domain is the whole tangent bundle TM and its fundamental tensor g is positive-definite. However, in many cases (for example, the well-known Kropina and Matsumoto metrics), these two…

For every Finsler metric $F$ we associate a Riemannian metric $g_F$ (called the Binet-Legendre metric). The transformation $F \mapsto g_F$ is $C^0$-stable and has good smoothness properties, in contrast to previous constructions. The…

We focus on the classical open problem of the classification of K\"ahler-Einstein manifolds that can be K\"ahler immersed into a complex projective space endowed with the Fubini-Study metric. In particular, we will deal with such problem in…

In this note, we study F-purity of pairs, and show (as is the case with log canonicity) that F-purity is preserved at the F-pure threshold. We also characterize when F-purity is equivalent to sharp F-purity, an alternate notion of purity…

We present classical and recent results on K\"ahler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of stability (K-stability). These are the notes for the SMI…

We prove a version of Myers-Steenrod's theorem for Finsler manifolds under minimal regularity hypothesis. In particular we show that an isometry between $C^{k,\alpha}$-smooth (or partially smooth) Finsler metrics, with $k+\alpha>0$, $k\in…

In this paper we provide new necessary and sufficient conditions for the existence of K\"ahler-Einstein metrics on small deformations of a Fano K\"ahler-Einstein manifold. We also show that the Weil-Petersson metric can be approximated by…

This work presents a formalized proof of modal completeness for G\"odel-L\"ob provability logic (GL) in the HOL Light theorem prover. We describe the code we developed, and discuss some details of our implementation, focusing on our choices…

Two Kaehler metrics on one complex manifold are said to be c-projectively equivalent if their J-planar curves, i.e., curves defined by the property that their acceleration is complex proportional to their velocity, coincide. The degree of…

In this paper, we study the continuity of rational functions realized by B\"uchi finite state transducers. It has been shown by Prieur that it can be decided whether such a function is continuous. We prove here that surprisingly, it cannot…

This is the first of a sequence of two papers. Here, a simple algebraic characterization of the Fano manifolds in the class of homogeneous toric bundles over a flag manifold G^C/P is provided in terms of symplectic data. The result of this…

We prove the local classification of K\"ahler metrics with constant holomorphic sectional curvature by exploiting the geometry of the bundle of 1-jets of holomorphic functions.

In the 1930s, H. Hopf conjectured that a closed, even-dimensional manifold of positive sectional curvature has positive Euler characteristic. We show this under the additional assumption of an isometric $T^4$-action on the manifold,…