For d≥4 and 2≤n≤d−2, an n-Ahlfors–David regular measure in Rᵈ with uniformly L²-bounded positive hard truncations of its n-dimensional Riesz transform is uniformly n-rectifiable.
For d≥4 and 2≤n≤d−2, an n-Ahlfors–David regular measure in Rᵈ with uniformly L²-bounded positive hard truncations of its n-dimensional Riesz transform is uniformly n-rectifiable.
For d≥4 and 2≤n≤d−2, an n-Ahlfors–David regular measure in Rᵈ with uniformly L²-bounded positive hard truncations of its n-dimensional Riesz transform is uniformly n-rectifiable.
If correct, settles the remaining higher-codimension range of the David–Semmes Riesz-transform criterion.
Does L² boundedness of the Riesz transform force uniform rectifiability in higher codimension?
Publication dates and editorial changes.
OpenAI reports a higher-codimension Riesz-transform criterion for rectifiability
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