Boundary Operators Associated With the Sixth-Order GJMS Operator

We describe a set of conformally covariant boundary operators associated with the 6th-order Graham--Jenne--Mason--Sparling (GJMS) operator on a conformally invariant class of manifolds that includes compactifications of Poincaré–Einstein manifolds. This yields a conformally covariant energy functional for the 6th-order GJMS operator on such manifolds. Our boundary operators also provide a new realization of the fractional GJMS operators of order one, three, and five as generalized Dirichlet-to-Neumann operators. This allows us to prove some sharp Sobolev trace inequalities involving the interior $W^{3,2}$-seminorm, including an analogue of the Lebedev–Milin inequality on six-dimensional manifolds.

Agreement with locatives in Kinyarwanda: a comparative analysis

In Bantu languages such as Chichewa or Herero, locatives can function as subjects and show noun class agreement (in class 16, 17 or 18) with predicates and modifiers. In contrast, (preverbal) locatives in Sotho-Tswana and Nguni have been analysed as prepositional adjuncts, which cannot agree. Our paper compares locatives in Kinyarwanda (JD61) with locatives in these other Bantu languages and demonstrates that the Kinyarwanda locative system is essentially of the Chichewa/Herero type. We show that Kinyarwanda locatives are nominal in nature, can act as subjects, and agree with predicates and modifiers. However, even though Kinyarwanda has four locative noun classes (16, 17, 18 and 25), there is only one locative agreement marker (class 16ha-), which indiscriminately appears with all locatives, regardless of their noun class. We explain this fact by arguing that noun class features in Kinyarwanda do not participate in locative agreement; instead, the invariant class 16 marker expresses agreement with a generic feature [location] associated with all locatives. We offer a syntactic analysis of this peculiar aspect of Kinyarwanda locative agreement, and we propose a parameter that accounts for the relevant difference between Kinyarwanda and Chichewa/Herero-type Bantu languages.