Abstract
We consider a mean curvature flow in a cone,that is,a hypersurface in a cone which propagates toward the opening of the cone with normal velocity depend-ing on its mean curvature.In addition,the contact angle between the hypersurface and the cone boundary depending on its position.First,we construct a family of radially symmetric self-similar solutions.Then we use these solutions to give a priori estimates for the solutions of the initial boundary value problems,and show their global exis-tence.
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