Related papers: A rigidity theorem for small resolutions
Distance functions of metric spaces with lower curvature bound, by definition, enjoy various metric inequalities; triangle comparison, quadruple comparison and the inequality of Lang-Schroeder-Sturm. The purpose of this paper is to study…
Consider an orientable compact surface in three dimensional Euclidean space with minimum total absolute curvature. If the Gaussian curvature changes sign to finite order and satisfies a nondegeneracy condition along closed asymptotic…
An alternative proof of Eliashberg-Gromov's C^0-rigidity theorem is presented and a new notion of weak Lie brackets for Hamiltonian vector fields is proposed and compared.
In this paper we introduce the notion of rigidity for harmonic-Ricci solitons and we provide some characterizations of rigidity, generalizing some known results for Ricci solitons. In the compact case we are able to deal with not…
We prove a rigidity result for certain critical Z/2 eigensections of the Laplacian on S^2 associated to a flat real line bundle determined by a branch-point configuration. More precisely, we show that every minimal non-degenerate critical…
We study the problem of moduli stabilisation in explicit heterotic orbifold compactifications, whose spectra contain the MSSM plus some vector-like exotics that can be decoupled. Considering all the bulk moduli, we obtain the 4D low energy…
We discuss the problem of classifying birational extremal contractions of smooth threefolds where the canonical bundle is trivial along the curves contracted, in the case when a divisor is contracted to a point. We prove the analytic…
Let M be a compact manifold with boundary. In this paper, we discuss some rigidity theorems of metrics in a same conformal class that fixes the boundary and satisfy certain integral conditions on the the scalar curvatures and the mean…
Motivated by M-theory compactification on elliptic Calabi-Yau threefolds, we present a correspondence between networks of small resolutions for singular elliptic fibrations and Coulomb branches of five-dimensional N=1 gauge theories. While…
We study the real loci of toric degenerations of complex varieties with reducible central fibre. We show that the topology of such degenerations can be explicitly described via the Kato-Nakayama space of the central fibre as a log space. We…
We study Riemannian manifolds with boundary under a lower Bakry-E'mery Ricci curvature bound. In our weighted setting, we prove several rigidity theorems for such manifolds with boundary. We conclude a rigidity theorem for the inscribed…
We establish topological local rigidity for uniform lattices in compactly generated groups, extending the result of Weil from the realm of Lie groups. We generalize the classical local rigidity theorem of Selberg, Calabi and Weil to…
In the conformal class of Euclidean space, we give some volume comparison theorems with help of Q-curvature. Meanwhile, for compact four dimensional manifolds with non-negative scalar curvature, we give a volume rigidity theorem with…
In this paper, we investigate the geometries associated with 3-forms of various orbital types on a symplectic 6-manifold. We demonstrate that certain unstable 3-forms, which naturally emerge from specific degenerations of Calabi-Yau…
We generalize the recently proposed mechanism by Demirtas, Kim, McAllister and Moritz arXiv:1912.10047 for the explicit construction of type IIB flux vacua with $|W_0|\ll 1$ to the region close to the conifold locus in the complex structure…
We study the large volume limit of the scalar potential in Calabi-Yau flux compactifications of type IIB string theory. Under general circumstances there exists a limit in which the potential approaches zero from below, with an associated…
Using the Jacobian matrix, we obtain theoretical expression of rigidity and the density of states of two-dimensional amorphous solids consisting of frictional grains in the linear response to an infinitesimal strain, in which we ignore the…
We prove two gluing theorems for special Lagrangian (SL) conifolds in complex space C^m. Conifolds are a key ingredient in the compactification problem for moduli spaces of compact SLs in Calabi-Yau manifolds. In particular, our theorems…
The purpose of this note is to show that the regular locus of a complex variety is locally parabolic at the singular set. This yields that the regular locus of a compact complex variety, e.g., of a projective variety, is parabolic. We give…
We describe the geometry of noncommutative deformations of local Calabi-Yau threefolds, showing that the choice of Poisson structure strongly influences the geometry of the quantum moduli space.