论文标题
Nirenberg圆锥形奇点的问题
The Nirenberg Problem for Conical Singularities
论文作者
论文摘要
我们提出了一种新的方法，即针对2个圆锥形的高斯曲率开出高斯曲率的问题，至少三个圆锥形奇异性和角度小于$2π$，主要的结果是班级的正功能至少是$ c^2 $的正常函数，以使其成为这种相结合的圆形圆锥体的高斯曲率。我们的方法与变异方法特别不同，因为它们不依赖于Moser-trudinger不平等。一路上，我们还证明了至少三个圆锥形奇异性和角度小于2 $π$的紧凑式Riemann表面的一般预发定理。
We propose a new approach to the question of prescribing Gaussian curvature on the 2-sphere with at least three conical singularities and angles less than $2π$, the main result being sufficient conditions for a positive function of class at least $C^2$ to be the Gaussian curvature of such a conformal conical metric on the round sphere. Our methods particularly differ from the variational approach in that they don't rely on the Moser-Trudinger inequality. Along the way, we also prove a general precompactness theorem for compact Riemann surfaces with at least three conical singularities and angles less than 2$π$.
