Regularity for the Optimal Transportation Problem with Euclidean Distance Squared Cost on the Embedded Sphere

نویسندگان

  • Jun Kitagawa
  • Micah Warren
چکیده

We give a sufficient condition on initial and target measures supported on the sphere S to ensure the solution to the optimal transport problem with the cost |x−y| 2 2 is a diffeomorphism.

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

On the Regularity of Optimal Transportation Potentials on round Spheres

In this paper the regularity of optimal transportation potentials dened on round spheres is investigated. Speci cally, this research generalises the calculations done by Loeper, where he showed that the strong (A3) condition of Trudinger and Wang is satis ed on the round sphere, when the cost-function is the geodesic distance squared. In order to generalise Loeper's calculation to a broader cla...

متن کامل

On the regularity of maps solutions of optimal transportation problems

We give a necessary and sufficient condition on the cost function so that the map solution of Monge’s optimal transportation problem is continuous for arbitrary smooth positive data. This condition was first introduced by Ma, Trudinger and Wang [17, 21] for a priori estimates of the corresponding Monge-Ampère equation. It is expressed by a socalled cost-sectional curvature being non-negative. W...

متن کامل

Regularity of Optimal Transport Maps

In the special case “cost=squared distance” on R, the problem was solved by Caffarelli [Caf1, Caf2, Caf3, Caf4], who proved the smoothness of the map under suitable assumptions on the regularity of the densities and on the geometry of their support. However, a major open problem in the theory was the question of regularity for more general cost functions, or for the case “cost=squared distance”...

متن کامل

Parabolic Optimal Transport Equations on Manifolds

We study a parabolic equation for finding solutions to the optimal transport problem on compact Riemannian manifolds with general cost functions. We show that if the cost satisfies the strong MTW condition and the stay-away singularity property, then the solution to the parabolic flow with any appropriate initial condition exists for all time and it converges exponentially to the solution to th...

متن کامل

Continuity of optimal transport maps and convexity of injectivity domains on small deformations of S

Given a compact Riemannian manifold, we study the regularity of the optimal transport map between two probability measures with cost given by the squared Riemannian distance. Our strategy is to define a new form of the so-called Ma-Trudinger-Wang condition and to show that this condition, together with the strict convexity on the nonfocal domains, implies the continuity of the optimal transport...

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:
  • SIAM J. Math. Analysis

دوره 44  شماره 

صفحات  -

تاریخ انتشار 2012