论文标题
一棵广义的费马特 - 甲状腺树，在表面上获得了潜意识
A generalized Fermat-Torricelli tree that has acquired a subconscious on a surface
论文作者
论文摘要
我们研究了在r中的a，b <k <b <k <b <k <b，在r中的c^2完整的表面m上的无限大地测量三角形的普遍化问题，以使三个地理位置的相交点（广义的fermat-torricelli点）在r中获得了s subseciels a poterialiald（supceptires a sipcectectious）。 s.ft问题的解决方案是一种广义的fermat-torricelli树，其中一个节点已经获得了潜意识。该解决方案基于与弧长相对于弧长的长度长度的新变化方法，该方法与在k <0或0 <k <c的表面上的第一个变异公式相吻合。反向s.ft问题的“可塑性”解决方案在广义的fermat-torricelli点f上与高斯曲率k（f）的绝对值与Geodesic Triangle的Aleksandrov曲率的绝对值通过获得G.ft点的潜意识来获得了Aleksandrov曲率的绝对值。
We study a generalized Fermat-Torricelli (S.FT) problem for infinitesimal geodesic triangles on a C^2 complete surface M with variable Gaussian curvature a < K < b, for a, b in R, such that the intersection point (generalized Fermat-Torricelli point) of the three geodesics acquires a positive real number (subconscious). The solution of the S.FT problem is a generalized Fermat-Torricelli tree with one node that has acquired a subconscious. This solution is based on a new variational method of the length of a geodesic arc with respect to arc length, which coincides with the first variational formula for geodesics on a surface with K < 0, or 0 < K < c. The 'plasticity' solution of the inverse S.FT problem gives a connection of the absolute value of the Gaussian curvature K(F) at the generalized Fermat-Torricelli point F with the absolute value of the Aleksandrov curvature of the geodesic triangle by acquiring both of them the subconscious of the g.FT point.
