Sharp Sobolev Inequalities via Projection Averages.

A family of sharp Sobolev inequalities is established by averaging the length of -dimensional projections of the gradient of a function. Moreover, it is shown that each of these new inequalities directly implies the classical  Sobolev inequality of Aubin and Talenti and that the strongest member of this family is the only affine invariant one among them-the affine  Sobolev inequality of Lutwak, Yang, and Zhang. When , the entire family of new Sobolev inequalities is extended to functions of bounded variation to also allow for a complete classification of all extremal functions in this case.

The Steiner formula for Minkowski valuations.

A Steiner type formula for continuous translation invariant Minkowski valuations is established. In combination with a recent result on the symmetry of rigid motion invariant homogeneous bivaluations, this new Steiner type formula is used to obtain a family of Brunn-Minkowski type inequalities for rigid motion intertwining Minkowski valuations.

Broadband terahertz imaging with highly sensitive silicon CMOS detectors.

This paper investigates terahertz detectors fabricated in a low-cost 130 nm silicon CMOS technology. We show that the detectors consisting of a nMOS field effect transistor as rectifying element and an integrated bow-tie coupling antenna achieve a record responsivity above 5 kV/W and a noise equivalent power below 10 pW/Hz(0.5) in the important atmospheric window around 300 GHz and at room temperature.