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math.AG2026
Rank-one convexity, polyconvexity, and extremality for three-dimensional elasticity tensors in various symmetry classes
Davit Harutyunyan, Gagik Amirkhanyan
It has been known that, for quadratic functions, quasiconvexity equals rank-one convexity but need not equal polyconvexity. While there is an explicit characterization of polyconve…
math.AG2021★ 2 cited
On the extreme rays of the cone of quasiconvex quadratic forms: Extremal determinats vs extremal and polyconvex forms
Davit Harutyunyan, Narek Hovsepyan
This work is concerned with the study of the extreme rays of the convex cone of quasiconvex quadratic forms (denoted by ). We characterize quadratic forms $…
math.AG2015
Towards characterization of all extremal quasiconvex quadratic forms
Davit Harutyunyan, Graeme W. Milton
Given a quasiconvex quadratic form, we prove that if the determinant of its acoustic tensor is an irreducible extremal polynomial that is not identically zer…