English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present simple conditions which ensure that a strongly elliptic operator$L$ generates an analytic semigroup on H\"older spaces on an arbitrary completemanifold of bounded geometry. This is done by establishing the equivalentproperty that $L$ is "sectorial", a condition that specifies the decay of theresolvent $(\lambda I - L)^{-1}$ as $\lambda$ diverges from the H\"olderspectrum of $L$. As one step, we prove existence of this resolvent if $\lambda$is sufficiently large, and on this general class of manifolds, use a geometricmicrolocal version of the semiclassical pseudodifferential calculus. Theproperties of $L$ and $e^{-tL}$ we obtain can then be used to provewellposedness of a wide class of nonlinear flows. We illustrate this by provingwellposedness on H\"older spaces of the flow associated to the ambientobstruction tensor on complete manifolds of bounded geometry.

Wellposedness of nonlinear flows on manifolds of bounded geometry