AI 中文总结
该研究分析受哈密顿扰动的Fueter方程解序列的气泡形成，结合Walpuski紧性定理等证明极限哈密顿量属无限余维特殊子集，表明其气泡形成高度非通用。
AI 中文摘要
我们研究受哈密顿扰动的Fueter方程解序列的气泡形成。根据Walpuski的紧性定理，有界能量序列弱收敛到一个Fueter映射，其能量损失由支撑在余二维可求长集上的缺陷测度记录。假设极限映射无非可去奇点，且气泡形成轨迹包含非平凡Lipschitz弧、气泡沿该弧附着于极限映射，我们证明该极限哈密顿量属于无限余维的特殊子集。证明结合了超凯勒流形中有理扫描轨迹的定量控制与横截性论证。我们期望Lipschitz弧与附着假设可自动成立，这强烈表明：在无非可去奇点的情况下，受哈密顿扰动的Fueter映射的气泡形成是高度非通用的。
英文摘要
We study bubbling for sequences of solutions of the Hamiltonian-perturbed Fueter equation. By Walpuski's compactness theorem, a bounded-energy sequence converges weakly to a Fueter map, with energy loss recorded by a defect measure supported on a codimension-two rectifiable set. Assuming that the limiting map has no non-removable singularities, the bubbling locus contains a nontrivial Lipschitz arc and the bubbles attach to the limiting map along this arc, we show that the limiting Hamiltonian lies in an exceptional subset of infinite codimension. The proof combines quantitative control of rational sweepout loci in hyperkähler manifolds with a transversality argument. We expect both the Lipschitz-arc and attachment assumptions to be automatic. This strongly suggests that, in the absence of non-removable singularities, bubbling of Hamiltonian-perturbed Fueter maps is highly nongeneric.
Comments20 pages, comments welcome
