Global climate change is causing glaciers to shrink, and in some cases, to vanish completely. Glaciers in Norway are no exception. Glacier inventories, archived imagery and topographic maps across Norway help trace the decadal evolution of individual glaciers. This study focuses on Breifonn (59.75°N, 6.89°E), the southernmost glacier in Norway. Using photogrammetric analyses of historical aerial photography, satellite data and uncrewed aerial vehicle data, we quantify how Breifonn has changed from its ‘pre-industrial’ Little Ice Age extent to its present size. Our geomorphology-based glacier reconstruction indicates that Breifonn covered an area of 5.8 ± 1.2 km2 during the Little Ice Age. Its main part reduced in area from 3.3 ± 0.3 km2 in 1955 to 0.17 ± 0.02 km2 in 2024 (94%) and has thinned on average by 0.4 ± 0.02 m a−1 between 1978 and 2019. Since the 1980s, the glacier has fragmented into several disconnected ice bodies. If current melt rates persist, Breifonn may disappear entirely soon.

The purpose of the paper is twofold. First, we show that partial-data transmission eigenfunctions associated with a conductive boundary condition vanish locally around a polyhedral or conic corner in $\mathbb{R}^n$, $n=2,3$. Second, we apply the spectral property to the geometrical inverse scattering problem of determining the shape as well as its boundary impedance parameter of a conductive scatterer, independent of its medium content, by a single far-field measurement. We establish several new unique recovery results. The results extend the relevant ones in [26] in two directions: first, we consider a more general geometric setup where both polyhedral and conic corners are investigated, whereas in [26] only polyhedral corners are concerned; second, we significantly relax the regularity assumptions in [26] which is particularly useful for the geometrical inverse problem mentioned above. We develop novel technical strategies to achieve these new results.