Related papers: Gamma-reduction for smooth orbifolds

We construct Morse-Smale-Witten complex for an effective orientable orbifold. For a global quotient orbifold, we also construct a Morse-Bott complex. We show that certain type of critical points of a Morse function has to be discarded to…

In this short note, we use classic computations for K\"ahler-Ricci flow to achieve scalar curvature bound for minimal manifold of general type.

Let (M,J) be a minimal compact complex surface of Kaehler type. It is shown that the smooth 4-manifold M admits a Riemannian metric of positive scalar curvature iff (M,J) admits a KAEHLER metric of positive scalar curvature. This extends…

We provide results on the smoothness of normalisers in connected reductive algebraic groups $G$ over fields $k$ of positive characteristic $p$. Specifically we we give bounds on $p$ which guarantee that normalisers of subalgebras of…

We establish generic regularity results for isoperimetric regions in closed Riemannian manifolds of dimension eight. In particular, we show that every isoperimetric region has a smooth nondegenerate boundary for a generic choice of smooth…

We establish a regularity result for the metric on any 4-dimensional extremal K\"ahler manifold, and a weak compactness theorem on the space of such metrics. Specifically, the sectional curvature at a point is bounded when the quantity…

In this note we briefly present the results of our computation of special K\"ahler geometry for polynomial deformations of Berglund-H\"ubsch type Calabi-Yau manifolds. We also build mirror symmetric Gauge Linear Sigma Model and check that…

We develop a general deformation principle for families of Riemannian metrics on smooth manifolds with possibly non-compact boundary, preserving lower scalar curvature bounds. The principle is used in order to strengthen boundary…

In this note, we make two methodical observations. $\bullet$ We prove in a simple explicit way that a necessary and sufficient condition for a K\"ahler manifold to be hyperk\"ahler is $h_{i\bar k} h_{j\bar l } \Omega^{\bar k \bar l} \ =\ C…

We construct explicitly a finite cover of the moduli stack of compact Riemann surfaces with a given group of symmetries by a smooth quasi-projective variety.

We give a complete description of the vertex algebra of global sections of the chiral de Rham complex of an arbitrary compact Ricci-flat K\"ahler manifold.

We describe smooth compactifications of certain families of reductive homogeneous spaces such as group manifolds for classical Lie groups, or pseudo-Riemannian analogues of real hyperbolic spaces and their complex and quaternionic…

We prove that Riemannian metrics with a uniform weak norm can be smoothed to having arbitrarily high regularity. This generalizes all previous smoothing results. As a consequence we obtain a generalization of Gromov's almost flat manifold…

Under a partially linear models we study a family of robust estimates for the regression parameter and the regression function when some of the predictor variables take values on a Riemannian manifold. We obtain the consistency and the…

In this paper, we show that every $8$-dimensional closed Riemmanian manifold with $C^\infty$-generic metrics admits a smooth minimal hypersurface. This generalized previous results by N. Smale and Chodosh-Liokumovich-Spolaor. Different from…

We study reduction of generalized complex structures. More precisely, we investigate the following question. Let $J$ be a generalized complex structure on a manifold $M$, which admits an action of a Lie group $G$ preserving $J$. Assume that…

Motivated by understanding the limiting case of a certain systolic inequality we study compact Riemannian manifolds having all harmonic 1-forms of constant length. We give complete characterizations as far as K\"ahler and hyperbolic…

Let $\tilde{\Sigma}$ be the universal cover of a closed surface $\Sigma$ of genus at least $2$. We characterize all equivariantly area-minimizing maps from $\tilde{\Sigma}$ to a Hilbert sphere, which are equivariant with respect to an…

The aim of the note is to extend the uniformization theorem to compact Kahler spaces X with mild singularities and establish a kind of rigidity of their universal coverings. We assume the fundamental group of X is large, residually finite…

The purpose of this paper is to establish a partial regularity theory on certain homogeneous complex Monge-Ampere equations. As consequences of this new theory, we prove the uniqueness of extremal Kaehler metrics and give an necessary…