Constructs lattice point sets with many rectangles and few isosceles triangles to produce explicit counterexamples to the Mizohata-Takeuchi conjecture for the paraboloid via transference principles.
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3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
years
2026 3verdicts
UNVERDICTED 3representative citing papers
Proves local well-posedness for Schrödinger map flow from T^d to S^2 at σ > d/2 + 1/2 (d≥3) and to general compact Kähler N at σ > d/2 + 5/6 (d≥2), first such low-regularity result in periodic setting.
Proves norm inflation for cubic hyperbolic NLS on T^2 in H^s for s ≤ 1/2 (s ≠ 0), establishing ill-posedness below the scaling-critical regularity s=1/2 in contrast to local well-posedness for s > 1/2.
citing papers explorer
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Rectangles, triangles and Schr\"{o}dinger waves
Constructs lattice point sets with many rectangles and few isosceles triangles to produce explicit counterexamples to the Mizohata-Takeuchi conjecture for the paraboloid via transference principles.
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Low-regularity Schr\"odinger map flow on high-dimensional periodic domains
Proves local well-posedness for Schrödinger map flow from T^d to S^2 at σ > d/2 + 1/2 (d≥3) and to general compact Kähler N at σ > d/2 + 5/6 (d≥2), first such low-regularity result in periodic setting.
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Norm inflation for the cubic hyperbolic NLS on $\mathbb T^2$
Proves norm inflation for cubic hyperbolic NLS on T^2 in H^s for s ≤ 1/2 (s ≠ 0), establishing ill-posedness below the scaling-critical regularity s=1/2 in contrast to local well-posedness for s > 1/2.