相关论文: On the impossibility of four-dimensional complex-h…

In this note we prove infinite dimensionality of the Teichm\"uller space of a hyperbolic Riemann surface lamination of a compact space having a simply connected leaf.

We give a new construction of Einstein and Kaehler-Einstein manifolds which are asymptotically complex hyperbolic, inspired by the work of Mazzeo-Pacard in the real hyperbolic case. The idea is to develop a gluing theorem for 1-handle…

Standard arguments state that Bose Einstein condensation (BEC) cannot occur in dimensions lower than three in the thermodynamic limit as the expressions for the number of bosons in the excited states are unbounded. These arguments imply…

We give a Khovanov homology proof that hyperbolic twist knots do not admit non-trivial Dehn surgeries with finite fundamental group.

We prove that every Einstein metric on the unit ball B^4 of C^2, asymptotic to the Bergman metric, is equal to it up to a diffeomorphism. We need a solution of Seiberg--Witten equations in this infinite volume setting. Therefore, and more…

We prove that a $4-$dimensional $C^2$ conformally compact Einstein manifold with H\"older continuous scalar curvature and with $C^{m,\alpha}$ boundary metric has a $C^{m,\alpha}$ compactification. We also study the regularity of the new…

We construct higher-dimensional generalizations of the Eguchi-Hanson gravitational instanton in the presence of higher-curvature deformations of general relativity. These spaces are solutions to Einstein gravity supplemented with the…

Let M be a hyperbolic n-manifold whose cusps have torus cross-sections. In arXiv:0901.0056, the authors constructed a variety of nonpositively and negatively curved spaces as "2\pi-fillings" of M by replacing the cusps of M with compact…

We obtain strong upper bounds for the Betti numbers of compact complex-hyperbolic manifolds. We use the unitary holonomy to improve the results given by the most direct application of the techniques of [DS17]. We also provide effective…

We prove that there is no power-counting renormalizable nonabelian generalization of the abelian topological mass mechanism in four dimensions. The argument is based on the technique of consistent deformations of the master equation…

A broad class of higher dimensional instanton solutions are found for a theory which contains gravity, a scalar field and antisymmetric tensor fields of arbitrary rank. The metric used, a warp product of an arbitrary number of any compact…

We show that under certain conditions, a nontrivial Riemannian submersion from positively curved four manifolds does not exist. This gives a partial answer to a conjecture due to Fred Wilhelm. We also prove a rigidity theorem for Riemannian…

It has been proposed that quantum complexity is dual to the volume of the extremal surface, the action of the Wheeler-DeWitt patch, and the spacetime volume of the patch. Recently, a generalized volume-complexity observable was formulated…

We study infinitesimal Einstein deformations on compact flat manifolds and on product manifolds. Moreover, we prove refinements of results by Koiso and Bourguignon which yield obstructions on the existence of infinitesimal Einstein…

Based on a well-known fact that there are no Einstein hypersurfaces in a non-flat complex space form, in this article we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hyersurface of a…

We construct the effective theory of the universal Kaehler modulus in warped compactifications using the Hamiltonian formulation of general relativity. The spacetime dependent 10d solution is constructed at the linear level for both the…

Any $6$-dimensional strict nearly K\"ahler manifold is Einstein with positive scalar curvature. We compute the coindex of the metric with respect to the Einstein-Hilbert functional on each of the compact homogeneous examples. Moreover, we…

We summarize our proof that the "Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime" introduced in Phys. Rev. Lett. 124, 081301 (2020) does not have consistent field equations, as such the theory does not exist. The proof is given…

We solve the Wheeler-DeWitt equation for {\it four}-dimensional Einstein gravity as an expansion in powers of the Planck mass by means of a heat kernel regularization. Our results suggest that in the universe with a very small radius or…

There are many ways of embedding a 4D spacetime in a given higher-dimensional manifold while, satisfying the field equations. In this work we extend and generalize a recent paper by Mashhoon and Wesson ({\it Gen. Rel. Gravit.} {\bf 39},…