Next Point-of-Interest (POI) recommendation aims to predict users' next locations by leveraging historical check-in sequences. Although existing methods have shown promising results, they often struggle to capture complex high-order relationships and effectively adapt to diverse user behaviors, particularly when addressing the cold-start issue. To address these challenges, we propose Hypergraph-enhanced Meta-learning Adaptive Network (HyperMAN), a novel framework that integrates heterogeneous hypergraph modeling with a difficulty-aware meta-learning mechanism for next POI recommendation. Specifically, three types of heterogeneous hyperedges are designed to capture high-order relationships: user visit behaviors at specific times (Temporal behavioral hyperedge), spatial correlations among POIs (spatial functional hyperedge), and user long-term preferences (user preference hyperedge). Furthermore, a diversity-aware meta-learning mechanism is introduced to dynamically adjust learning strategies, considering users behavioral diversity. Extensive experiments on real-world datasets demonstrate that HyperMAN achieves superior performance, effectively addressing cold start challenges and significantly enhancing recommendation accuracy.