关于differential forms的$L^p$不等式和$p>>1$的半代数集的$L^p$上同调
On $L^p$ inequality for differential forms and $L^p$ cohomology of a semialgebraic set for $p>>1$
摘要：
研究了$p>>1$的$\R^n$的紧半代数子集上的Poincaré型$L^p$不等式.首先利用Lipschitz形变收缩得到一个局部不等式及其导数的估计。然后，利用二重复形技巧，将局部不等式推广为整体不等式。由此得到正规紧半代数伪流形的$L^p$上同调与奇异上同调之间的同构。
英文摘要：
We study Poincaré type $L^p$ inequality on a compact semialgebraic subset of $\R^n$ for $p>>1$. First we derive a local inequality by using a Lipschitz deformation retraction with estimates on its derivatives. Then, we extend the local inequality to a global inequality by employing double complex technique. As a consequence we obtain an isomorphism between $L^p$ cohomology and singular cohomology of a normal compact semialgebraic pseudomanifold.
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