论文标题
参数不平等和weyl定律的体积光谱
Parametric inequalities and Weyl law for the volume spectrum
论文作者
论文摘要
我们表明，由格罗莫夫（Gromov）猜想的紧凑式riemannian歧管中的weyl定律可以从两种著名不平等的参数概括中得出：等等不平等和coarea不平等。我们证明了在低维度中的两个这样的概括，并获得了3个manifolds中1个周期的Weyl定律。我们还提供了Almgren同构定理的新证明。
We show that the Weyl law for the volume spectrum in a compact Riemannian manifold conjectured by Gromov can be derived from parametric generalizations of two famous inequalities: isoperimetric inequality and coarea inequality. We prove two such generalizations in low dimensions and obtain the Weyl law for 1-cycles in 3-manifolds. We also give a new proof of the Almgren isomorphism theorem.
