Displaying similar documents to “On a Carathéodory's conjecture on umbilics : representing ovaloids”

Planar vector field versions of Carathéodory's and Loewner's conjectures.

Carlos Gutiérrez, Federico Sánchez Bringas (1997)

Publicacions Matemàtiques

Similarity:

Let r = 3, 4, ... , ∞, ω. The Cr-Carathéodory's Conjecture states that every Cr convex embedding of a 2-sphere into R3 must have at least two umbilics. The Cr-Loewner's conjecture (stronger than the one of Carathéodory) states that there are no umbilics of index bigger than one. We show that these two conjectures are equivalent to others about planar vector fields. For instance, if r ≠ ω, Cr...

The Bellows conjecture.

Connelly, R., Sabitov, I., Walz, A. (1997)

Beiträge zur Algebra und Geometrie

Similarity:

An update on a few permanent conjectures

Fuzhen Zhang (2016)

Special Matrices

Similarity:

We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture†, Lieb permanent dominance conjecture, Bapat and Sunder conjecture† on Hadamard product and diagonal entries, Chollet conjecture on Hadamard product, Marcus conjecture on permanent of permanents, and several other conjectures. Some of these conjectures are recently settled; some are still open.We...