Geometric Analysis by Ailana Fraser & André Neves & Peter M. Topping & Paul C. Yang

Author:Ailana Fraser & André Neves & Peter M. Topping & Paul C. Yang
Language: eng
Format: epub
ISBN: 9783030537258
Publisher: Springer International Publishing

Given (x, Z) ∈ SX i, i = 1, …, N, we have that

Hence, recalling the definition of the maps Φi, we have

Combining Claims 2 with 3 we deduce that for all

From Theorem 2.3.8 we have that

□

2.3.3 Min–Max Theory and the Volume Spectrum

Combining the Weyl Law for the Volume Spectrum 2.3.4 with Theorem 2.2.9 and Theorem 2.2.12 we obtain

Theorem 2.3.10

Assume (M n+1, g) is a closed Riemannian manifold, 3 ≤ (n + 1) ≤ 7.

For each there exist a smooth embedded cycle V  so that

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