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We estimate the upper bound for the $ell^{infty}$-norm of the volume form on $mathbb{H}^2timesmathbb{H}^2timesmathbb{H}^2$ seen as a class in $H_{c}^{6}(mathrm{PSL}_{2}mathbb{R}timesmathrm{PSL}_{2}mathbb{R}timesmathrm{PSL}_{2}mathbb{R};mathbb{R})$. This gives the lower bound for the simplicial volume of closed Riemennian manifolds covered by $mathbb{H}^{2}timesmathbb{H}^{2}timesmathbb{H}^{2}$. The proof of these facts yields an algorithm to compute the lower bound of closed Riemannian manifolds covered by $big(mathbb{H}^2big)^n$.
The Riemannian product of two hyperbolic planes of constant Gaussian curvature -1 has a natural Kahler structure. In fact, it can be identified with the complex hyperbolic quadric of complex dimension two. In this paper we study Lagrangian surfaces i
We prove the positive energy conjecture for a class of asymptotically Horowitz-Myers metrics on $mathbb{R}^{2}timesmathbb{T}^{n-2}$. This generalizes the previous results of Barzegar-Chru{s}ciel-H{o}rzinger-Maliborski-Nguyen as well as the authors.
It is known that for $Omega subset mathbb{R}^{2}$ an unbounded convex domain and $H>0$, there exists a graph $Gsubset mathbb{R}^{3}$ of constant mean curvature $H$ over $Omega $ with $partial G=$ $partial Omega $ if and only if $Omega $ is included i
For the moduli space of unmarked convex $mathbb{RP}^2$ structures on the surface $S_{g,m}$ with negative Euler characteristic, we investigate the subsets of the moduli space defined by the notions like boundedness of projective invariants, area, Grom
This survey aims to give a brief introduction to operator theory in the Hardy space over the bidisc $H^2(mathbb D^2)$. As an important component of multivariable operator theory, the theory in $H^2(mathbb D^2)$ focuses primarily on two pairs of commu