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On a2m-dimensional closed manifold, we investigate the existence of prescribedQ-curvature metrics with conical singularities. We present here a general existence and multiplicity result in the supercritical regime. To this end, we first carry out a blow-up analysis of a2mth-order PDE associated to the problem, and then apply a variational argument of min-max type. Form>1, this seems to be the first existence result for supercritical conic manifolds different from the sphere. 

Abstract Most nanomedicines require efficient in vivo delivery to elicit meaningful diagnostic and therapeutic effects. However, en route to their intended tissues, systemically administered nanoparticles often encounter delivery barriers. To describe these barriers, the term “nanoparticle blood removal pathways” (NBRP) is proposed, which summarizes the interactions between nanoparticles and the body's various cell‐dependent and cell‐independent blood clearance mechanisms. Nanoparticle design and biological modulation strategies are reviewed to mitigate nanoparticle‐NBRP interactions. As these interactions affect nanoparticle delivery, the preclinical literature from 2011–2021 is studied, and the nanoparticle blood circulation and organ biodistribution data are analyzed. The findings reveal that nanoparticle surface chemistry affects the in vivo behavior more than other nanoparticle design parameters. Combinatory biological‐PEG surface modification improves the blood area under the curve by ≈418%, with a decrease in liver accumulation of up to 47%. A greater understanding of nanoparticle‐NBRP interactions and associated delivery trends will provide new nanoparticle design and biological modulation strategies for safer, more effective, and more efficient nanomedicines.