We prove the existence of free boundary minimal annuli inside suitably convex subsets of three-dimensional Riemannian manifolds with nonnegative Ricci curvature − including strictly convex domains of the Euclidean space R.

We define the notions of strong convexity and strong visibility. These notions generalize standard convexity and visibility, as well as several types of nontraditional convexity, such as iso-oriented rectangles and C-oriented polygons. We explore the properties of strong convexity and strong visibility in two and three dimensions. In particular, we establish analogs of the following properties ...

We address the problem of verifying PCTL properties of Markov Decision Processes whose state transition probabilities are only known to lie within uncertainty sets. Using results from convex theory and duality, we propose a suite of verication algorithms and prove their soundness, completeness and termination when arbitrary convex models of uncertainty are considered. Furthermore, soundness and...

A fundamental problem in systems biology consists of investigating robustness properties of genetic regulatory networks (GRNs) with respect to model uncertainty. This paper addresses this problem for GRNs where the coefficients are rationally affected by polytopic uncertainty, and where the saturation functions are not exactly known. First, it is shown that a condition for ensuring that the GRN...

A robust resource allocation (RA) algorithm for cognitive relay networks with multiple primary users considering joint channel uncertainty and interference uncertainty is proposed to maximize the capacity of the networks subject to the interference threshold limitations of primary users’ receivers (PU-RXs) and the total power constraint of secondary user’s transmitter and relays. Ellipsoid set ...

This paper considers the problem of finding a controller for a discrete time linear periodically time-varying system with structured parametric uncertainty which achieves robust ‘2 semi-norm performance (the equivalent of robust H2 norm performance for time-varying systems). This problem is shown to be a generalization of a guaranteed cost control problem when the structure of the uncertainty i...