论文信息 - Double bubbles in Gauss space and spheres

Double bubbles in Gauss space and spheres

We prove that a standard Y is an area-minimizing partition of Gauss space into three given volumes, provided that the standard double bubble is an area-minimizing partition of high-dimensional spheres. We prove that the standard double bubble is the area-minimizing partition of spheres of any dimension where the volumes differ by at most 4%

[1] D. Stroock,et al. Probability Theory: An Analytic View , 1995, The Mathematical Gazette.

[2] M. Gromov,et al. Isoperimetry of Waists and Concentration of Maps , 2003 .

[3] V. Sudakov,et al. Extremal properties of half-spaces for spherically invariant measures , 1978 .

[4] Michael Hutchings,et al. The structure of area-minimizing double bubbles , 1997 .

[5] C. Borell. The Brunn-Minkowski inequality in Gauss space , 1975 .

[6] D. Freeman,et al. The double bubble problem in spherical and hyperbolic space , 2002 .

[7] Ben W. Reichardt,et al. Proof of the Double Bubble Conjecture in R4 and certain higher dimensional cases , 2003 .

[8] F. Barthe. Extremal Properties of Central Half-Spaces for Product Measures , 2001 .

[9] Michael Hutchings,et al. Proof of the Double Bubble Conjecture , 2002 .