For harmonic functions in R^n, ε-smallness of the gradient on a set of Hausdorff dimension n-2+δ (any δ > 0) forces a C ε^α bound on the half-ball, reaching the sharp threshold and answering the Logunov-Malinnikova conjecture.
Title resolution pending
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.AP 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Propagation of smallness near codimension two for gradients of harmonic functions
For harmonic functions in R^n, ε-smallness of the gradient on a set of Hausdorff dimension n-2+δ (any δ > 0) forces a C ε^α bound on the half-ball, reaching the sharp threshold and answering the Logunov-Malinnikova conjecture.