论文标题
在圆柱体中翻译广义平均曲率流的溶液：I。恒定边界角度
Translating Solutions of a Generalized Mean Curvature Flow in a Cylinder: I. Constant Boundary Angles
论文作者
论文摘要
我们研究了涉及平均曲率和驱动力的正力的广义平均曲率流。在本文中，我们首先构建各种径向对称的翻译溶液，然后选择其中一个以满足圆柱体中规定的边界角度。然后，我们考虑以初始超出表面启动的流量：显示A先验估计值（尤其是平均曲率的均匀及时界限，保证了相应的完全非线性方程的均匀抛物性），从而为初始边界值问题解决方案提供了整体存在，并将其融合到相应的翻译解决方案中。我们的研究提供了有关维度的影响，平均曲率的力量，驱动力和边界角度对径向对称翻译溶液的存在和稳定性的完整阐述。
We study a generalized mean curvature flow involving a positive power of the mean curvature and a driving force. In this paper, we first construct all kinds of radially symmetric translating solutions, and then select one of them to satisfy a prescribed boundary angle in a cylinder. We then consider the flow starting at an initial hypersurface: showing the a priori estimates (especially the uniform-in-time bounds for the mean curvature which guarantee the uniform parabolicity of the corresponding fully nonlinear equation), giving the global existence for the solution of the initial boundary value problem, and proving its convergence to the corresponding translating solution. Our study provides a complete exposition on the influence of the dimension, the power of the mean curvature, the driving force and the boundary angles on the existence and stability of radially symmetric translating solutions.
