Author

S. Kim

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Preprint Aug 2026

The unit ball of quadratic forms on an octagonal sector

Let \[\mathfrak O=\{(x,y)\in[0,1]^2:x+y\le \sqrt2\} \] be the first-quadrant sector of a regular octagon. For quadratic forms \(P(x,y)=ax^2+bxy+cy^2\), we study the supremum norm over \(\mathfrak O\). We obtain a complete five-region formula for the norm, according to whether the norming contact occurs at an endpoint o...

Manwook Han, S. Kim, G. A. Muñoz-Fernández et al. · 1 citation · ⚡1

Preprint Aug 2026

Classical polynomial inequalities for quadratic forms on an octagonal sector

We establish a collection of sharp inequalities for real quadratic forms on the first-quadrant sector of a regular octagon. Starting from the complete extreme-point description of the associated polynomial unit ball, we compute the exact pointwise Bernstein function for the Euclidean gradient. One extreme curve control...

Manwook Han, S. Kim, J. B. Seoane-Sep'ulveda · 1 citation