Related papers: Llarull type theorems for bands in Three and Four …
We study the relation between the quantum geometry of wave functions and the Landau level (LL) spectrum of two-band Hamiltonians with a quadratic band crossing point (QBCP) in two-dimensions. By investigating the influence of interband…
We show how to define curvature as a measure using the Gauss-Bonnet Theorem on a family of singular surfaces obtained by gluing together smooth surfaces along boundary curves. We find an explicit formula for the curvature measure as a sum…
We extend the class of recently formulated scalar-nonmetricity theories by coupling a five-parameter nonmetricity scalar to a scalar field and considering a mixed kinetic term between the metric and the scalar field. The symmetric…
We discuss some classical and quantum properties of 2d gravity models involving metric and a scalar field. Different models are parametrized in terms of a scalar potential. We show that a general Liouville-type model with exponential…
We compute the scalar curvature of a curved noncommutative 3-torus. To perturb the flat metric, the standard volume form on the noncommutative 3-torus is conformally perturbed and the corresponding perturbed Laplacian is analyzed. Using…
We generalize the maximal diameter sphere theorem due to Toponogov by means of the radial curvature. As a corollary to our main theorem, we prove that for a complete connected Riemannian $n$-manifold $M$ having radial sectional curvature at…
We use a reformulation of topological group field theories in 3 and 4 dimensions in terms of variables associated to vertices, in 3d, and edges, in 4d, to obtain new scaling bounds for their Feynman amplitudes. In both 3 and 4 dimensions,…
We define pure gauge $QCD$ on an infinite strip of width $L$. Techniques similar to those used in finite $TQCD$ allow us to relate $3D$-observables to pure $QCD_2$ behaviors. The non triviality of the $L \arrow 0$ limit is proven and the…
Bray's football theorem (\cite{bray2009penrose}) is a weakening of Bishop theorem in dimension 3. It gives a sharp volume upper bound for a three dimensional manifold with scalar curvature larger than $n(n-1)$ and Ricci curvature larger…
The classical theory of Laplace is not suitable for describing the behavior of microscopic bubbles. The theory of second gradient fluids (which are able to exert shear stresses in equilibrium conditions) allows us to obtain a new expression…
We consider a capillary drop that contacts several planar bounding walls so as to produce singularities (vertices) in the boundary of its free surface. It is shown under various conditions that when the number of vertices is less than or…
It is shown that the geometry of parallelizable manifolds can be extended to non-parallelizable ones by extending the connection that a global frame field would define on a parallelizable manifold to a connection that a singular frame field…
In this paper the Randall-Sundrum model with brane-localized curvature terms is considered. Within some range of parameters a compact extra dimension in this model can be astronomically large. In this case the model predicts small deviation…
We prove a surface embedding theorem for 4-manifolds with good fundamental group in the presence of dual spheres, with no restriction on the normal bundles. The new obstruction is a Kervaire-Milnor invariant for surfaces and we give a…
We give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing the maximal distance between $(n+1)$ points in infinitesimally small neighborhoods of a point. Since this characterization is purely in…
The equations of General Relativity are recast in the form of a wave equation for the Weyl tensor. This allows to reformulate gravitational wave theory in terms of curvature waves, rather than metric waves. The existence of two transverse…
We determine bounds on the curvature of local patches of spacetime from the requirement of intact long-range chiral symmetry. The bounds arise from a scale-dependent analysis of gravitational catalysis and its influence on the effective…
The dynamics of a thin liquid film on the underside of a curved cylindrical substrate is studied. The evolution of the liquid layer is investigated as the film thickness and the radius of curvature of the substrate are varied. A…
Given an eigenvalue $\lambda$ of the Laplace-Beltrami operator on $n-$spheres or $-$hemispheres, with multiplicity $m$ such that $\lambda=\lambda_{k}=\dots = \lambda_{k+m-1}$, we characterise the lowest and highest orders in the set…
In this paper we provide a sharp characterization of the smooth four-dimensional sphere. The assumptions of the theorem are conformally invariant, and can be reduced to an L^2 inequality of the Weyl tensor and positivity of the Yamabe…