A complete smooth nonnegatively Ricci-curved metric on Euclidean space in dimension 16 has more harmonic functions of pointwise polynomial growth at most integer degree 50000 than Euclidean space has harmonic polynomials of that degree.
A complete smooth nonnegatively Ricci-curved metric on Euclidean space in dimension 16 has more harmonic functions of pointwise polynomial growth at most integer degree 50000 than Euclidean space has harmonic polynomials of that degree.
A complete smooth nonnegatively Ricci-curved metric on Euclidean space in dimension 16 has more harmonic functions of pointwise polynomial growth at most integer degree 50000 than Euclidean space has harmonic polynomials of that degree.
If correct, disproves the integer-degree form of Yau’s harmonic-dimension comparison question.
Can nonnegative Ricci curvature allow more integer-degree harmonic functions than Euclidean space?
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OpenAI reports a counterexample to integer-degree harmonic dimension comparison
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