Search for neutral MSSM Higgs bosons decaying to a pair of tau leptons in pp collisions

Peer reviewe

Measurement of top quark–antiquark pair production in association with a W or Z boson in pp collisions at √s=8 TeV

Peer reviewe

Searches for electroweak production of charginos, neutralinos, and sleptons decaying to leptons and W, Z, and Higgs bosons in pp collisions at 8 TeV

Peer reviewe

Measurement of prompt J/ψ pair production in pp collisions at √s = 7 Tev

Peer reviewe

Study of hadronic event-shape variables in multijet final states in pp collisions at √s=7 TeV

Peer reviewe

Constraints on parton distribution functions and extraction of the strong coupling constant from the inclusive jet cross section in pp collisions at √s=7 TeV

Peer reviewe

Mean curvature bounds and eigenvalues of Robin Laplacians

We consider the Laplacian with attractive Robin boundary conditions, $$Q^\Omega_\alpha u=-\Delta u, \quad \dfrac{\partial u}{\partial n}=\alpha u \text{ on } \partial\Omega,$$ in a class of bounded smooth domains $\Omega \in\mathbb{R}^\nu$; here $n$ is the outward unit normal and $\alpha>0$ is a constant. We show that for each $j\in\mathbb{N}$ and $\alpha\to+\infty$, the $j$th eigenvalue $E_j(Q^\Omega_\alpha)$ has the asymptotics $$E_j(Q^\Omega_\alpha)=-\alpha^2 -(\nu-1)H_\mathrm{max}(\Omega)\,\alpha+{\mathcal O}(\alpha^{2/3}),$$ where $H_\mathrm{max}(\Omega)$ is the maximum mean curvature at $\partial \Omega$. The discussion of the reverse Faber-Krahn inequality gives rise to a new geometric problem concerning the minimization of $H_\mathrm{max}$. In particular, we show that the ball is the strict minimizer of $H_\mathrm{max}$ among the smooth star-shaped domains of a given volume, which leads to the following result: if $B$ is a ball and $\Omega$ is any other star-shaped smooth domain of the same volume, then for any fixed $j\in\mathbb{N}$ we have $E_j(Q^B_\alpha)>E_j(Q^\Omega_\alpha)$ for large $\alpha$. An open question concerning a larger class of domains is formulated