The Double Bubble Conjecture

نویسندگان

  • JOEL HASS
  • MICHAEL HUTCHINGS
  • ROGER SCHLAFLY
  • Richard Schoen
چکیده

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 2π/3.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Proof of the Double Bubble Conjecture

The least-area hypersurface enclosing and separating two given volumes in R is the standard double bubble.

متن کامل

On the oriented perfect path double cover conjecture

‎An  oriented perfect path double cover (OPPDC) of a‎ ‎graph $G$ is a collection of directed paths in the symmetric‎ ‎orientation $G_s$ of‎ ‎$G$ such that‎ ‎each arc‎ ‎of $G_s$ lies in exactly one of the paths and each‎ ‎vertex of $G$ appears just once as a beginning and just once as an‎ ‎end of a path‎. ‎Maxov{'a} and Ne{v{s}}et{v{r}}il (Discrete‎ ‎Math‎. ‎276 (2004) 287-294) conjectured that ...

متن کامل

Proof of the Double Bubble Conjecture

We prove that the standard double bubble provides the least-area way to enclose and separate two regions of prescribed volume in R3.

متن کامل

PROOF OF THE DOUBLE BUBBLE CONJECTURE 461 For

We prove that the standard double bubble provides the least-area way to enclose and separate two regions of prescribed volume in R3.

متن کامل

Double Bubbles in the 3 - Torus

We present a conjecture, based on computational results, on the area minimizing way to enclose and separate two arbitrary volumes in the flat cubic three-torus T 3. For comparable small volumes, we prove that an area minimizing double bubble in T 3 is the standard double bubble from R 3 .

متن کامل

Heat transfer enhancement due to air bubble injection into a horizontal double pipe heat exchanger

If an air flow is injected into a liquid fluid, many ambulant air bubbles are formed inside the fluid. Air bubbles move inside the liquid fluid because of the buoyancy force, and the mobility of these air bubbles makes sizable commixture and turbulence inside the fluid. This mechanism was employed to enhance the heat transfer rate of a horizontal double pipe heat exchanger in this paper. Howeve...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1996