An automated algorithm is presented to determine the DNA molecule intrinsic curvature profiles and the molecular spatial orientations in Atomic Force Microscope images. The curvature is composed by static and dynamic contributions. The first one is the intrinsic curvature, vectorial function of the DNA nucletide sequence, while the second one is due to thermal noise. This algorithm allows to re...

All continuous linearly intertwining symmetric Blaschke valuations on convex bodies are completely classified. It is shown that there is a unique non-trivial such valuation. On symmetric bodies, this valuation is the curvature image operator.

We estimate from below by geometric data the eigenvalues of the periodic Sturm-Liouville operator ?4 d 2 ds 2 + 2 (s) with potential given by the curvature of a closed curve.

An invariant cone in the space of curvature operators is one that is preserved by a flow. For Ricci flow, the condition R ≥ 0 is preserved in all dimensions, while the conditionR ≤ 0 is preserved only in real dimension two. Positive curvature operator is preserved in all dimensions [11], but positive sectional curvature is not preserved in dimensions four and above. The known counterexamples, c...

The purpose of this paper is fourfold: (1) to introduce and study a second order PDE, determined accidentally by a Riemann wave, reflecting the connection between oriented parallelograms area and sectional curvature on Riemannian manifolds; (2) to introduce and study the asymptotic behavior of oriented parallelograms area controlled by the sectional curvature; (3) to study some partial differen...