Flat forms, bi-Lipschitz parametrizations, and smoothability of manifolds

We give a sufficient condition for a metric (homology) manifold to be locally bi-Lipschitz equivalent to an open subset in \rn. The condition is a Sobolev condition for a measurable coframe of flat 1-forms. In combination with an earlier work of D. Sullivan, our methods also yield an analytic characterization for smoothability of a Lipschitz manifold in terms of a Sobolev regularity for frames in a cotangent structure. In the proofs, we exploit the duality between flat chains and flat forms, and recently established differential analysis on metric measure spaces. When specialized to \rn, our result gives a kind of asymptotic and Lipschitz version of the measurable Riemann mapping theorem as suggested by Sullivan

Asymptotic paths for subsolutions of quasilinear elliptic equations

Let u be an entire lower semicontinuous subsolution to the quasilinear elliptic equation div A(x ,∇ u )=0 in ℝ n . It is shown that if u is not bounded above, then there exists a path going to infinity along which u tends to infinity. The result extends works of Talpur, Fuglede, and others. Growth aspects of subsolutions are also studied.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46647/1/229_2005_Article_BF01357721.pd

BLD-mappings in W2,2W^{2,2} are locally invertible

We prove that mappings of bounded length distortion are local homeomorphisms if they have -integrable weak second derivatives.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41936/1/208-318-2-391_03180391.pd

Smooth quasiregular mappings with branching

We give an example of a -smooth quasiregular mapping in 3-space with nonempty branch set. Moreover, we show that the branch set of an arbitrary quasiregular mapping in n -space has Hausdorff dimension quantitatively bounded away from n . By using the second result, we establish a new, qualitatively sharp relation between smoothness and branching.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47944/1/10240_2004_Article_24.pd

Pre-use phase LCA of a multi-story residential building: Can greenhouse gas emissions be used as a more general environmental performance indicator?

Both the construction and use of buildings cause significant environmental pressures. The greenhouse gas (GHG) emissions imposed by buildings have been studied rather extensively, but less is known about other impacts. Still, climate change is only one harmful impact driven by buildings. Furthermore, no studies exist about how the other impacts are correlated with GHG emissions in the building context, and thus to what extent GHGs could be utilized as a more general environmental performance indicator. This paper fills these gaps by presenting a life cycle assessment of the pre-use phase of a modern concrete-element residential building with a very comprehensive life cycle inventory (LCI). The focus of the study is on the comparison of the accumulation of different environmental impacts relative to GHGs. The accumulation is analyzed from two perspectives common to building LCAs: building systems and different construction materials. The ReCiPe midpoint assessment method is utilized to reach wide impact category coverage. The study shows how GHGs act as a relatively good indicator for eight impact categories, but not for the others. The study also depicts that a very high coverage in the LCI must be reached to capture the majority of the different impacts. Many materials and building systems are considered non-relevant and are often excluded from building LCAs, which are in fact of great importance in many impact categoriesThe Academy of Finland (Grant 286747)Peer reviewed pre-printRitrýnt tímari