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1. Proof of the Michael–Simon–Sobolev inequality using optimal transport

   https://doi.org/10.1515/crelle-2023-0054  

   Brendle, Simon; Eichmair, Michael (August 2023, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract We give an alternative proof of the Michael–Simon–Sobolev inequality using techniques from optimal transport. The inequality is sharp for submanifolds of codimension 2. 

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2. Urban form and structure explain variability in spatial inequality of property flood risk among US counties

   https://doi.org/10.1038/s43247-024-01337-3  

   Ma, Junwei; Mostafavi, Ali (December 2024, Communications Earth & Environment)

   Abstract Understanding the relationship between urban form and structure and spatial inequality of property flood risk has been a longstanding challenge in urban planning and emergency management. Here we explore eight urban form and structure features to explain variability in spatial inequality of property flood risk among 2567 US counties. Using datasets related to human mobility and facility distribution, we identify notable variation in spatial inequality of property flood risk, particularly in coastline and metropolitan counties. The results reveal variations in spatial inequality of property flood risk can be explained based on principal components of development density, economic activity, and centrality and segregation. The classification and regression tree model further demonstrates how these principal components interact and form pathways that explain spatial inequality of property flood risk. The findings underscore the critical role of urban planning in mitigating flood risk inequality, offering valuable insights for crafting integrated strategies as urbanization progresses. 

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3. Arakelov inequalities in higher dimensions

   https://doi.org/10.1515/crelle-2023-0075  

   Kovács, Sándor J; Taji, Behrouz (November 2023, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract We develop a Hodge theoretic invariant for families of projective manifolds that measures the potential failure of an Arakelov-type inequality in higher dimensions, one that naturally generalizes the classical Arakelov inequality over regular quasi-projective curves.We show that, for families of manifolds with ample canonical bundle, this invariant is uniformly bounded.As a consequence, we establish that such families over a base of arbitrary dimension satisfy the aforementioned Arakelov inequality, answering a question of Viehweg. 

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4. Frontier workers and the seedbeds of inequality and prosperity

   https://doi.org/10.1093/jeg/lbad018  

   Connor, Dylan_Shane; Kemeny, Tom; Storper, Michael (August 2023, Journal of Economic Geography)

   Abstract This article examines the role of work at the cutting of technological change—frontier work—as a driver of prosperity and spatial income inequality. Using new methods and data, we analyze the geography and incomes of frontier workers from 1880 to 2019. Initially, frontier work is concentrated in a set of ‘seedbed’ locations, contributing to rising spatial inequality through powerful localized wage premiums. As technologies mature, the economic distinctiveness of frontier work diminishes, as ultimately happened to cities like Manchester and Detroit. Our work uncovers a plausible general origin story of the unfolding of spatial income inequality. 

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5. Income inequality in the United States, 1975–2022

   https://doi.org/10.1111/1475-5890.12368  

   Hardy, Bradley L; Krause, Elizabeth; Ziliak, James P (June 2024, Fiscal Studies)

   Abstract We examine trends in household disposable income inequality and potential mechanisms shaping inequality through changes to work, wages, earnings, marriage, and the tax and transfer system in the United States over the nearly five‐decade period from 1975 to 2022. Overall after‐tax and transfer income inequality increased more than 25 per cent since the mid‐1970s, and by as much as 50 per cent when comparing the 90^thand 10^thpercentiles. While there has been substantial upgrading in formal education credentials among both men and women – an inequality‐reducing development – those with fewer credentials have increasingly been less likely to work and marry, each of which could result in higher inequality. The latter effects are exacerbated by those selecting into marriage and cohabitation being more likely to partner with those holding similar educational credentials and earning power. Moreover, the decline in work among the less skilled coincided with the transformation of the safety net to rewarding work. These demographic and policy changes have resulted in a pulling apart of the US income distribution. 

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