Related papers: The Kummer tensor density in electrodynamics and i…

We develop a degree theory for compact immersed hypersurfaces of prescribed $K$-curvature immersed in a compact, orientable Riemannian manifold, where $K$ is any elliptic curvature function. We apply this theory to count the (algebraic)…

For a standard graded ring $R$ of dimension $\geq 2$ over a perfect field of characteristic $p>0$ and a homogeneous ideal $I$ of finite colength, the HK density function of $R$ with respect to $I$ is a compactly supported continuous…

The problem of obtaining an explicit representation for the fourth invariant of geodesic motion (generalized Carter constant) of an arbitrary stationary axisymmetric vacuum spacetime generated from an Ernst Potential is considered. The…

We prove that a Kummer surface defined over a complete strictly Henselian discretely valued field $K$ of residue characteristic different from 2 admits a strict Kulikov model after finite base change. The Kulikov models we construct will be…

We revisit an emergent gravity scenario in $(4+1)$ dimensions underlying a propagating geometric torsion ${\cal H}_3$ with a renewed interest. We show that a pair-symmetric $4$th order curvature tensor is sourced by a two-form Neveu-Schwarz…

We describe the "hyperbolic" properties of a riemann surface lamination M canonically associated to every compact three manifolds of curvature less than 1. More precisely, if the geodesic flow is the phase space attached to an ordinary…

Given a convex disk $K$ and a positive integer $k$, let $\delta_T^k(K)$ and $\delta_L^k(K)$ denote the $k$-fold translative packing density and the $k$-fold lattice packing density of $K$, respectively. Let $T$ be a triangle. In a very…

We prove that any hyper-K\"{a}hler sixfold $K$ of generalized Kummer type has a naturally associated manifold $Y_K$ of $\mathrm{K}3^{[3]}$-type. It is obtained as crepant resolution of the quotient of $K$ by a group of symplectic…

We derive a tensorial formula for a fourth-order conformally invariant differential operator on conformal 4-manifolds. This operator is applied to algebraic Weyl tensor densities of a certain conformal weight, and takes its values in…

We show that a large subclass of 3d $\mathcal{N}=4$ quiver gauge theories consisting of unitary and special unitary gauge nodes with only fundamental/bifundamental matter have multiple Seiberg-like IR duals. A generic quiver $\mathcal{T}$…

Unlike general relativity, scalar-tensor theories of gravity predict scalar gravitational waves even from a spherically symmetric gravitational collapse. We solve numerically the generation and propagation of the scalar gravitational wave…

We investigate geodesics in specific Kundt type N (or conformally flat) solutions to Einstein's equations. Components of the curvature tensor in parallelly transported tetrads are then explicitly evaluated and analyzed. This elucidates some…

We demonstrate that the unitarity of quantum field theory, through the positivity of spectral functions, underlies thermodynamic irreversibility for a subsystem separated by a horizon, in direct analogy with the irreversibility of…

We use weighted polynomial approximation to prove the existence of a compact set K with non-empty interior and a function f is dense in the space A(K) of all continuous functions on K that are holomorphic in the interior of K, endowed with…

Motivated by the growing interest in the nonmetricity-matter couplings, we develop the scalar-tensor formulation of recently introduced $f(Q,T)$ gravity, where $Q$ is the nonmetricity and $T$ is the trace of the energy-momentum tensor. The…

It is conjectured that for every convex disks K, the translative covering density of K and the lattice covering density of K are identical. It is well known that this conjecture is true for every centrally symmetric convex disks. For the…

We analyze the generic structure of Einstein tensor projected onto a 2-D spacelike surface S defined by unit timelike and spacelike vectors u_i and n_i respectively, which describe an accelerated observer (see text). Assuming that flow…

The tensor power of the clique on $t$ vertices (denoted by $K_t^n$) is the graph on vertex set $\{1, ..., t\}^n$ such that two vertices $x, y \in \{1, ..., t\}^n$ are connected if and only if $x_i \neq y_i$ for all $i \in \{1, ..., n\}$.…

In this paper, we develop a quantum theory of homogeneously curved tetrahedron geometry, by applying the combinatorial quantization to the phase space of tetrahedron shapes defined in arXiv:1506.03053. Our method is based on the relation…

I discuss some aspects of the moduli space of hyper-K{\"a}hler four-fold compactifications of type II and ${\cal M}$- theories. The dimension of the moduli space of these theories is strictly bounded from above. As an example I study…