论文标题
小鹰能量和小球的临界表面的局部叶子
Local foliations by critical surfaces of the Hawking energy and small sphere limit
论文作者
论文摘要
Lamm，Metzger和Schulze和Ikoma，Machiodi和Mondino在三维Riemannian歧管上限制了威尔莫尔表面的地方叶面，这些叶子的叶子特别是鹰型能量的关键表面，以防它们完全包含在完全的地层型超过型超塞式甲状腺液中。我们将这些叶子概括为非全面测量空间类高表面的一般情况，从而构建了霍金能量的临界临界表面的独特局部叶面。弗里德里希（Friedrich）在评估霍金能量的所谓小球时极限时的差异。他研究了霍金能量的临界临界表面的浓度，并获得了显然与霍洛维茨和施密特鹰鹰能量良好的小球极限不同的结果，任何准局部能量必须满足这个小球体的限制。我们独立确认差异，并解释其发生的原因。我们还证明，这些表面适合在lamm，metzger和Schulze的意义上评估霍金能量，并且我们发现这些表面可能会导致测量能量的过量。
Local foliations of area constrained Willmore surfaces on a 3-dimensional Riemannian manifold were constructed by Lamm, Metzger and Schulze, and Ikoma, Machiodi and Mondino, the leaves of these foliations are, in particular, critical surfaces of the Hawking energy in case they are contained in a totally geodesic spacelike hypersurface. We generalize these foliations to the general case of a non-totally geodesic spacelike hypersurface, constructing a unique local foliation of area constrained critical surfaces of the Hawking energy. A discrepancy when evaluating the so called small sphere limit of the Hawking energy was found by Friedrich. He studied concentrations of area constrained critical surfaces of the Hawking energy and obtained a result that apparently differs from the well established small sphere limit of the Hawking energy of Horowitz and Schmidt, this small sphere limit in principle must be satisfied by any quasi local energy. We independently confirm the discrepancy and explain the reasons for it to happen. We also prove that these surfaces are suitable to evaluate the Hawking energy in the sense of Lamm, Metzger and Schulze, and we find an indication that these surfaces may induce an excess in the energy measured.
