Add to ORKGAbstract. The classical isoperimetric inequality states that the surface of smallest area enclosing a given volume in R3 is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 2=3. 1
We prove that the standard double bubble is the minimizing double bubble in R4 and in certain higher...
The classic double bubble theorem says that the least-perimeter way to enclose and separate two pres...
Abstract. We prove a new type of universal inequality between the diastole, defined using a minimax ...
The classical isoperimetric inequality in R^3 states that the surface of smallest area encl...
ABSTRACT. An area minimizing double bubble in R n is given by two (not necessarily connected) region...
An area minimizing double bubble in $\mathbb R^n$ is given by two (not necessarily connected) region...
We prove that the standard double bubble is the least-area way to enclose and separate two regions o...
We prove that the standard double bubble provides the least-area way to enclose and separate two reg...
The least-area hypersurface enclosing and separating two given volumes in R^n is the standard double...
13 pages, 4 figures. Prepared on behalf of the participants in the Clay Mathematics Institute Summer...
In 2008 Reichardt proved that the optimal Euclidean double bubble---the least-perimeter way to enclo...
On the line with density |x|^p, we prove that the best single bubble is an interval with endpoint at...
We study the isoperimetric problem on ℝ1 with a prescribed density function f(x)=|x|. Under these co...
We present a conjecture, based on computational results, on the area minimizing way to encl...
We use a new approach that we call unification to prove that standard weighted double bubbles in n-d...
We prove that the standard double bubble is the minimizing double bubble in R4 and in certain higher...
The classic double bubble theorem says that the least-perimeter way to enclose and separate two pres...
Abstract. We prove a new type of universal inequality between the diastole, defined using a minimax ...
The classical isoperimetric inequality in R^3 states that the surface of smallest area encl...
ABSTRACT. An area minimizing double bubble in R n is given by two (not necessarily connected) region...
An area minimizing double bubble in $\mathbb R^n$ is given by two (not necessarily connected) region...
We prove that the standard double bubble is the least-area way to enclose and separate two regions o...
We prove that the standard double bubble provides the least-area way to enclose and separate two reg...
The least-area hypersurface enclosing and separating two given volumes in R^n is the standard double...
13 pages, 4 figures. Prepared on behalf of the participants in the Clay Mathematics Institute Summer...
In 2008 Reichardt proved that the optimal Euclidean double bubble---the least-perimeter way to enclo...
On the line with density |x|^p, we prove that the best single bubble is an interval with endpoint at...
We study the isoperimetric problem on ℝ1 with a prescribed density function f(x)=|x|. Under these co...
We present a conjecture, based on computational results, on the area minimizing way to encl...
We use a new approach that we call unification to prove that standard weighted double bubbles in n-d...
We prove that the standard double bubble is the minimizing double bubble in R4 and in certain higher...
The classic double bubble theorem says that the least-perimeter way to enclose and separate two pres...
Abstract. We prove a new type of universal inequality between the diastole, defined using a minimax ...