Piotr Hajłasz

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20232025

most cited

C^{2}

-Lusin approximation of strongly convex functions

1 citations · 1 across the 4 of their papers we have counts for

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math.CA2025

$C^{2}$ -Lusin approximation of convex functions: one variable case

Paweł Goldstein, Piotr Hajłasz

We prove that if $f : (a, b) \to R$ is convex, then for any $ε > 0$ there is a convex function $g \in C^{2} (a, b)$ such that $∣ {f \neq = g} ∣ < ε$ and $\Vert f-g\Vert…

math.CA2024

$C^{2}$ -Lusin approximation of strongly convex bodies

Daniel Azagra, Marjorie Drake, Piotr Hajłasz

We prove that, if $W \subset R^{n}$ is a locally strongly convex body (not necessarily compact), then for any open set $V \supset \partial W$ and $ε > 0$ , and $V \su…

math.CA2023★ 1 cited

$C^{2}$ -Lusin approximation of strongly convex functions

Daniel Azagra, Marjorie Drake, Piotr Hajłasz

We prove that if $u : R^{n} \to R$ is strongly convex, then for every $ε > 0$ there is a strongly convex function $v \in C^{2} (R^{n})$ such that $|\{u\neq v…

math.CA2023

A geometric approach to second-order differentiability of convex functions

Daniel Azagra, Anthony Cappello, Piotr Hajłasz

We show a new, elementary and geometric proof of the classical Alexandrov theorem about the second order differentiability of convex functions. We also show new proofs of recent re…

C2-Lusin approximation of convex functions: one variable case

C2-Lusin approximation of strongly convex bodies

C2-Lusin approximation of strongly convex functions

A geometric approach to second-order differentiability of convex functions

$C^{2}$ -Lusin approximation of convex functions: one variable case

$C^{2}$ -Lusin approximation of strongly convex bodies

$C^{2}$ -Lusin approximation of strongly convex functions