Geometry of interactions in complex bodies

Bodies, Interactions, and Hypercomputation1

After sketching the role of embodiment in present models of intelligent computer-based systmes, and making some notes concerning the computational power of the emboidied systemst, the contribution proposes EG-systems as a suitable formal framework for study some of the relevant properties of embodied autonomous agents acting in computationally complicated environments, and provides a result con...

Ground States in Complex Bodies

A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappinngs and Cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and Cartesian currents describe the inner substructure of the material elements. Balanc...

Complex intersection bodies

We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann’s theorem to the complex case by proving that complex intersection bodies of symmetric complex convex bodies are also convex. Other results include stability in the complex Busemann-Petty problem for arbitrary measures an...

The complex geometry of

Analogues of Complex Geometry

We prove that there is no hope of trying to invent pseudoholomorphic theories of anything other than curves, even if one allows more general objects than almost complex manifolds. The hard part is dispensing with theories of pseudoholomorphic hypersurfaces; hypersurface theories exist “microlocally” (in abundance) but not “locally.”