The Structure of Gaussian Minimal Bubbles
The Structure of Gaussian Minimal Bubbles
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DOI：
10.1007/s12220-020-00531-x
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发表时间：
2018-05
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影响因子：
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通讯作者：
Steven M. Heilman
中科院分区：
文献类型：
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作者：
Steven M. Heilman
证明了具有固定高斯体积的m个不交集按最小高斯表面积划分一定是-维的。这是从使用无穷小平移的第二个变分论证得出的。特殊情况证明了高斯测度下的双泡问题，并给出了一个额外的技术假设。也就是说，当三个最小集合是相邻的120度扇区时。技术假设是最小化集合的三重连接点具有多项式体积增长。再次假定技术假设，我们证明了高斯测度下的三重气泡猜想。我们的方法结合联合收割机的高斯极小曲面的Colding-Minicozzi理论与一些参数中使用的Hutchings-Morgan-Ritoré-Ros证明的欧几里德双泡猜想。
It is shown thatmdisjoint sets with fixed Gaussian volumes that partitionwith minimum Gaussian surface area must be-dimensional. This follows from a second variation argument using infinitesimal translations. The special caseproves the Double Bubble problem for the Gaussian measure, with an extra technical assumption. That is, when, the three minimal sets are adjacent 120 degree sectors. The technical assumption is that the triple junction points of the minimizing sets have polynomial volume growth. Assuming again the technical assumption, we prove theTriple Bubble Conjecture for the Gaussian measure. Our methods combine the Colding–Minicozzi theory of Gaussian minimal surfaces with some arguments used in the Hutchings–Morgan–Ritoré-Ros proof of the Euclidean Double Bubble Conjecture.