https://neckpinch.com/authors/louis-yudowitz/New arXiv papers by Louis Yudowitz, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2509.26515arxiv:2509.26515Tue, 30 Sep 2025 00:00:00 GMTAlexander Mramor, Louis Yudowitz — We construct an embedded ancient solution to the mean curvature flow which is qualitatively given by a "stack" of two ancient pancakes joined by a neck. Our solution is closed, non-convex, and contained in a slab.Mean curvature flowAncient solutions https://arxiv.org/abs/2408.10751arxiv:2408.10751Tue, 20 Aug 2024 00:00:00 GMTLouis Yudowitz — We prove lower and upper semi-continuity of the Morse index for sequences of gradient Ricci shrinkers which bubble tree converge in the sense of past work by the author and Buzano. Our proofs rely on adapting recent arguments of Workman which were used to study certain sequences of CMC hypersurfaces and were in turn adapted from work on Da Lio-Gianocca-Riviere. Moreover, we are able to refine Workman's methods by using techniques related to polynomially weighted Sobolev spaces. This all also requires us to extend the analysis to handle when the shrinkers we study are non-compact, which we can do due to the availability of a suitable notion of finite weighted volume. Finally, we identify a technical condition which ensures the Morse index of an asymptotically conical shrinker is bounded below by the f-index of its asymptotic cone.Ricci solitonsBoundaries & non-compactMinimal & CMC surfacesDiscrete & graph Ricci https://arxiv.org/abs/2312.13011arxiv:2312.13011Wed, 20 Dec 2023 00:00:00 GMTKlaus Kroencke, Louis Yudowitz — We prove dynamical stability and instability theorems for Poincaré-Einstein metrics under the Ricci flow. Our key tool is a variant of the expander entropy for asymptotically hyperbolic manifolds, which Dahl, McCormick and the first author established in a recent article. It allows us to characterize stability and instability in terms of a local positive mass theorem and in terms of volume comparison for nearby metrics.Ricci flowRicci solitonsEinstein metricsStability & uniquenessBoundaries & non-compactPhysics https://arxiv.org/abs/2206.06791arxiv:2206.06791Tue, 14 Jun 2022 00:00:00 GMTReto Buzano, Louis Yudowitz — We prove bubble-tree convergence of sequences of gradient Ricci shrinkers with uniformly bounded entropy and uniform local energy bounds, refining the compactness theory of Haslhofer-Mueller. In particular, we show that no energy concentrates in neck regions, a result which implies a local energy identity for the sequence. Direct consequences of these results are an identity for the Euler characteristic and a local diffeomorphism finiteness theorem.Ricci solitonsLimit spaces & RCDDiscrete & graph Ricci