走向现代数学学术报告 - 陈优民博士（No. 588）

报告题目：Quantization for biharmonic maps from non-collapsed degenerating Einstein 4-manifolds

报告人：陈优民 博士（上海交通大学）

时间：2023年3月30日 上午10:30

地点：学术报告厅（工西416）

摘要:For a sequence of extrinsic biharmonic maps u _j : M _j→N from a sequence of non-collapsed degenerating closed Einstein 4-manifolds (M_ j ,g _j ) with bounded Einstein constants, bounded diameters and bounded L ^2 curvature energy into a compact Riemannian manifold (N,h) with uniformly bounded biharmonic energy, we establish a compactness theory modular finitely many bubbles, which are finite energy biharmonic maps from R ^4 , or from R ^4 /Γfor some nontrivial finite groupΓ⊂SO(4), or from some complete, noncompact, Ricci flat, non-flat ALE 4-manifold (orbifold). To achieve this, we develop a sophisticated asymptotic analysis for solutions over degenerating neck regions.