Un-unzippable Convex Caps
نویسنده
چکیده
An unzipping of a polyhedron P is a cut-path through its vertices that unfolds P to a non-overlapping shape in the plane. It is an open problem to decide if every convex P has an unzipping. Here we show that there are nearly flat convex caps that have no unzipping. A convex cap is a “top” portion of a convex polyhedron; it has a boundary, i.e., it is not closed by a base.
منابع مشابه
Boundary Torsion and Convex Caps of Locally Convex Surfaces
We prove that the torsion of any closed space curve which bounds a simply connected locally convex surface vanishes at least 4 times. This answers a question of Rosenberg related to a problem of Yau on characterizing the boundary of positively curved disks in Euclidean space. Furthermore, our result generalizes the 4 vertex theorem of Sedykh for convex space curves, and thus constitutes a far r...
متن کاملAddendum to: Edge-Unfolding Nearly Flat Convex Caps
This addendum to [O’R17] establishes that a nearly flat acutely triangulated convex cap in the sense of that paper can be edge-unfolded even if closed to a polyhedron by adding the convex polygonal base under the cap.
متن کاملOn weakly convex star-shaped polyhedra
Weakly convex polyhedra which are star-shaped with respect to one of their vertices are infinitesimally rigid. This is a partial answer to the question whether every decomposable weakly convex polyhedron is infinitesimally rigid. The proof uses a recent result of Izmestiev on the geometry of convex caps.
متن کاملA Variational Proof of Alexandrov's Convex Cap Theorem
We give a variational proof of the existence and uniqueness of a convex cap with the given upper boundary. The proof uses the concavity of the total scalar curvature functional on the space of generalized convex caps. As a byproduct, we prove that generalized convex caps with the fixed boundary are globally rigid, that is uniquely determined by their curvatures.
متن کاملCaps on Hermitian varieties and maximal curves
A lower bound for the size of a complete cap of the polar space H(n, q2) associated to the non-degenerate Hermitian variety Un is given; this turns out to be sharp for even q when n = 3. Also, a family of caps of H(n, q2) is constructed from Fq2-maximal curves. Such caps are complete for q even, but not necessarily for q odd.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1802.01621 شماره
صفحات -
تاریخ انتشار 2018