arXiv research

Study proves uniform ellipticity implies uniform polyconvexity for anisotropic energy functionals.

Polyconvex energies with conformal invariance have smooth stationary points outside a discrete set.

Constructs polyhedral chains with prescribed tangent plane distributions.

We study integrals of the form $\int_Ωf\left( dω\right)$, where $1\leq k\leq n$, $f:Λ^{k}\rightarrow\mathbb{R}$ is continuous and $ω$ is a $\left(k-1\right)$-form. We introduce the appropriate notions of convexity, namely ext. one convexity, ext. quasiconvexity and ext. polyconvexity. We study their relations, give sev…