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The Minkowski problem for the $k$-torsional rigidity
Xia Zhao, Peibiao Zhao
https://arxiv.org/abs/2505.24494 https://arxiv.org/pdf/25…

The Minkowski problem for the $k$-torsional rigidity
P. Salani [Adv. Math., 229 (2012)] introduced the $k$-torsional rigidity associated with a $k$-Hessian equation and obtained the Brunn-Minkowski inequalities $w.r.t.$ the torsional rigidity in $\mathbb{R}^3$. Following this work, we first construct, in the present paper, a Hadamard variational formula for the $k$-torsional rigidity with $1\leq k\leq n-1$, then we can deduce a $k$-torsional measure from the Hadamard variational formula. Based on the $k$-torsional measure, we propose the Minkowsk…

»Frauen und niedrig Gebildete skeptischer als Männer und höher Gebildete« - dieses Framing, ich könnte schreien! Frauen sind einer Doppelbelastung ausgesetzt und verdienen im Durchschnitt weniger, wie auch die »niedrig Gebildeten« körperlich belastende Arbeit zu geringerem Lohn beziehen und früher sterben.

The role of the Lorentz force in sunspot equilibrium
J. M. Borrero, A. Pastor Yabar, M. Schmassmann, M. Rempel, M. van Noort, M. Collados
https://arxiv.org/abs/2505.23986

The role of the Lorentz force in sunspot equilibrium
Sunspots survive on the solar surface for time-scales ranging from days to months. This requires them to be in an equilibrium involving magnetic fields and hydrodynamic forces. Unfortunately, theoretical models of sunspot equilibrium are very simplified as they assume that spots are static and possess a self-similar and axially symmetric magnetic field. These assumptions neglect the role of small scale variations of the magnetic field along the azimuthal direction produced by umbral dots, light…