What kind of applications does a StatefulSet manage?

StatefulSets are specifically designed to manage applications that require stable, unique network identifiers and persistent storage. This makes them ideal for stateful applications, where the application's state needs to be maintained across restarts, scaling, and upgrades.

In a StatefulSet, each pod has its own persistent storage that is not shared with other pods, allowing the application to retain its state and data even if the pod is deleted or rescheduled. This is crucial for applications such as databases or distributed systems that need to store data reliably.

In contrast, stateless applications do not require such persistence and can be deployed using other Kubernetes abstractions like Deployments. Batch processing applications might handle data temporarily and may not need the persistent characteristics managed by a StatefulSet. Finally, while microservices can be stateful or stateless, not all microservices require the specific features provided by StatefulSets.

Thus, the focus on persistent storage and the management of stateful applications make the correct answer the one that highlights applications requiring persistent storage.